ORIGINAL_ARTICLE
Stirling Numbers and Generalized Zagreb Indices
We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.
http://ijmc.kashanu.ac.ir/article_15092_b7bb85d9dbe4ac40d6d223adc42453dd.pdf
2017-03-01T11:23:20
2020-02-22T11:23:20
1
5
10.22052/ijmc.2017.15092
Simple Graph
Zagreb index
Stirling number
T.
Doslic
doslic@grad.hr
true
1
1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb,
1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb,
1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb,
AUTHOR
S.
Sedghi
sedghi_gh@yahoo.com
true
2
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, Iran
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, Iran
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, Iran
LEAD_AUTHOR
N.
Shobe
nabi_shobe@yahoo.com
true
3
Department of Mathematics, Babol Branch,
Islamic Azad
University, Babol, Iran
Department of Mathematics, Babol Branch,
Islamic Azad
University, Babol, Iran
Department of Mathematics, Babol Branch,
Islamic Azad
University, Babol, Iran
AUTHOR
1. E. Deutsch, S. Klavžar, M–polynomial and degree–based topological indices,
1
Iranian J. Math. Chem. 6 (2015) 93–102.
2
2. T. Došlić, M. Ghorbani, M. A. Hosseinzadeh, Eccentric connectivity polynomial of
3
some graph operations, Util. Math. 84 (2011) 297–309.
4
3. G. H. Fath–Tabar, A. Azad, N. Elahinezhad, Some topological indices of tetrameric
5
1,3–adamantane, Iranian J. Math. Chem. 1 (2010) 111–118.
6
4. B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015)
7
1184–1190.
8
5. R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison–Wesley,
9
Reading, 1988.
10
6. I. Gutman, K. Ch. Das, The first Zagreb index 30 years after, MATCH Commun.
11
Math. Comput. Chem. 50 (2004) 83–92.
12
7. I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total -electron
13
energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.
14
8. X. Li, J. Zheng, A unified approach to the extremal trees for different indices,
15
MATCH Commun. Math. Comput. Chem. 54 (2005) 195–208.
16
9. S. Sedghi, N. Shobe, M. A. Salahshoor, The polynomials of a graph, Iranian J.
17
Math. Sci. Inf. 3 (2008) 55–68.
18
10. G. B. A. Xavier, E. Suresh, I. Gutman, Counting relations for general Zagreb
19
indices, Kragujevac J. Math. 38 (2014) 95–103.
20
ORIGINAL_ARTICLE
Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matching polynomial, (-1)^km(G, k), in a regular graph. In the rest of this paper, we apply these relations for finding 5,6-matchings of fullerene graphs.
http://ijmc.kashanu.ac.ir/article_15093_be5ca1f23c477021c246d4c612236dc6.pdf
2017-03-01T11:23:20
2020-02-22T11:23:20
7
23
10.22052/ijmc.2017.15093
Characteristic polynomial
Matching polynomial
Fullerene graph
F.
Taghvaee
taghvaei19@yahoo.com
true
1
University of Kashan
University of Kashan
University of Kashan
AUTHOR
G.
Fath-Tabar
fathtabar@kashanu.ac.ir
true
2
University of Kashan
University of Kashan
University of Kashan
LEAD_AUTHOR
1. A. R. Ashrafi and G. H. FathTabar, Bounds on the Estrada index of ISR (4, 6)–
1
fullerenes, Appl. Math. Lett. 24 (2011) 337–339.
2
2. A. Behmaram, Matching in Fullerene and Molecular Graphs, Ph.D. thesis,
3
University of Tehran, 2013.
4
3. A. Behmaram, T. Došlić and S. Friedland, Matchings in m–generalized fullerene
5
graphs, Ars Math. Contemp. 11 (2016) 301–313.
6
4. A. Behmaram, H. Yousefi Azari and A. R. Ashrafi, Closed formulas for the number
7
of small paths, independent sets and matchings in fullerenes, Appl. Math. Lett. 25
8
(2012) 1721–1724.
9
5. A. Behmaram, On the number of 4matchings in graphs, MATCH Commun. Math.
10
Comput. Chem. 62 (2009) 381–388.
11
6. N. Biggs, Algebraic Graph Theory, Cambridge Univ. Press, Cambridge, 1974.
12
7. D. M. Cvetković, M. Doob and H. Sachs, Spectra of Graphs: Theory and
13
Applications, Academic Press, New York, 1980.
14
8. M. Deza, M. Dutour and P. W. Fowler, Zigzags, railroads and knots in fullerenes,
15
J. Chem. Inf. Comp. Sci. 44 (2004) 1282–1293.
16
9. E. J. Farrell, An introduction to matching polynomials, J. Combin. Theory Ser. B 27
17
(1979) 75–86.
18
10. G. H. FathTabar, A. R. Ashrafi and I. Gutman, Note on Estrada and L-Estrada
19
indices of graphs, Bull. Cl. Sci. Math. Nat. Sci. Math. 34 (2009) 1–16.
20
11. G. H. FathTabar, A. R. Ashrafi and D. Stevanović, Spectral properties of
21
fullerenes, J. Comput. Theor. Nanosci. 9 (2012) 327–329.
22
12. P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Oxford Univ. Press,
23
Oxford, 1995.
24
13. M. Ghorbani and E. BaniAsadi, Remarks on characteristic coefficients of
25
fullerene graphs, Appl. Math. Comput. 230 (2014) 428–435.
26
14. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl and R. E. Smalley, C60:
27
buckminsterfullerene, Nature 318 (1985) 162–163.
28
15. Z. Mehranian, A. Gholami and A. R. Ashrafi, Experimental results on the symmetry
29
and topology of 3 and 4generalized fullerenes, J. Comput. Theor. Nanosci. 11
30
(2014) 1–6.
31
16. W. Myrvold, B. Bultena, S. Daugherty, B. Debroni, S. Girn, M. Minchenko, J.
32
Woodcock and P. W. Fowler, FuiGui: A graphical user interface for investigating
33
conjectures about fullerenes, MATCH Commun. Math. Comput. Chem. 58 (2007)
34
403–422.
35
17. P. Schwerdtfeger, L. Wirz and J. Avery, Program fullerene: a software package for
36
constructing and analyzing structures of regular fullerenes, J. Comput. Chem. 34
37
(2013) 1508–1526.
38
18. M. D. Sikirić and M. Deza, Space fullerenes; computer search for new
39
FrankKasper structures II, Structural Chemistry, 23 (2012) 1103–1114.
40
19. M. D. Sikirić, O. DelgadoFriedrichs and M. Deza, Space fullerenes: a computer
41
search for new Frank–Kasper structures, Acta Crystallogr. A 66 (2010) 602–615.
42
20. F. Taghvaee and A. R. Ashrafi, Ordering some regular graphs with respect to
43
spectral moments, submitted.
44
21. F. Taghvaee and A. R. Ashrafi, On spectrum of Igraphs and its ordering with
45
respect to spectral moments, submitted.
46
22. F. Taghvaee and A. R. Ashrafi, Comparing fullerenes by spectral moments, J.
47
Nanosci. Nanotechnol. 16 (2016) 3132–3135.
48
23. F. Taghvaee and G. H. FathTabar, Signless Laplacian spectral moments of graphs
49
and ordering some graphs with respect to them, Alg. Struc. Appl. 1 (2014) 133–141.
50
24. R. Vesalian and F. Asgari, Number of 5-matching in graphs, MATCH Commun.
51
Math. Comput. Chem. 69 (2013) 33–46.
52
ORIGINAL_ARTICLE
The Topological Indices of some Dendrimer Graphs
In this paper the Wiener and hyper Wiener index of two kinds of dendrimer graphs are determined. Using the Wiener index formula, the Szeged, Schultz, PI and Gutman indices of these graphs are also determined.
http://ijmc.kashanu.ac.ir/article_15413_df8b2c0cfc3d418f4b890e723474b4cd.pdf
2017-03-01T11:23:20
2020-02-22T11:23:20
25
35
10.22052/ijmc.2017.15413
topological index
Dendrimer
Wiener index
Hyper Wiener index
M.
Darafsheh
true
1
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
AUTHOR
M.
Namdari
true
2
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
AUTHOR
S.
Shokrolahi
shokrolahisara@yahoo.com
true
3
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
LEAD_AUTHOR
1. R. Entringer, Distance in graphs: Trees, J. Combin. Math. Combin. Comput. 24
1
(1997) 65–84.
2
2. I. Gutman, S. Klavžar, B. Mohar (Eds), Fifty years of the Wiener index, MATCH
3
Commun. Math. Comput. Chem. 35 (1997) 1–259.
4
3. H. Hosoya, Topological Index, A Newly Proposed Quantity Characterizing the
5
Topological Nature of Structural Isomers of Saturated Hydrocarbons, Bull. Chem.
6
Soc. Jpn. 44 (1971) 2332–2339.
7
4. H. Wiener, Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc.
8
69 (1947) 17–20.
9
5. I. Gutman, A formula for the Wiener number of trees and its extension to graphs
10
containing cycles, Graph Theory Notes N.Y. 27 (1994) 9–15.
11
6. S. Klavžar, A. Rajapakse, I. Gutman, The Szeged and the Wiener index of graphs,
12
Appl. Math. Lett. 9 (1996) 45–49.
13
7. P. V. Khadikar, On a Novel structural descriptor PI, Nat. Acad. Sci. Lett. 23 (2000)
14
113–118.
15
8. P. V. Khadikar. S. Karmakar and V. K. Agrawal, Relationship and relative
16
correction potential of the Wiener, Szeged and PI Indices, Nat. Acad. Sci. Lett. 23
17
(2000) 165–170.
18
9. H. P. Schultz, T. P. Schultz, Topological organic chemistry. 3. Graph theory, Binary
19
and Decimal Adjacency Matrices, and Topological indices of Alkanes, J. Chem. Inf.
20
Comput. Sci. 31 (1991) 144–147.
21
10. H. P. Schultz, T. P. Schultz, Topological organic chemistry. 6. Theory and
22
topological indices of cycloalkanes, J. Chem. Inf. Comput. Sci. 33 (1993) 240–244.
23
11. I. Gutman, Selected properties of the Schultz molecular topological index, J. Chem.
24
Inf. Comput. Sci. 34 (1994) 1087–1089.
25
12. I. Gutman, Y. N. Yeh, S. L. Lee, Y. L. Luo, Some recent results in the theory of the
26
Wiener number, Indian J. Chem. 32 (1993) 651–661.
27
13. M. Randić, Novel molecular descriptor for structure–property studies, Chem. Phys.
28
Lett. 211 (1993) 478–483.
29
14. D. J. Klein, I. Lukovits, I. Gutman, On the definition of the hyper–Wiener index for
30
cycle-containing structures, J. Chem. Inf. Comput. Sci. 35 (1995) 5052.
31
ORIGINAL_ARTICLE
On the Multiplicative Zagreb Indices of Bucket Recursive Trees
Bucket recursive trees are an interesting and natural generalization of ordinary recursive trees and have a connection to mathematical chemistry. In this paper, we give the lower and upper bounds for the moment generating function and moments of the multiplicative Zagreb indices in a randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$. Also, we consider the ratio of the multiplicative Zagreb indices for different values of $n$ and $b$. All our results reduce to the ordinary recursive trees for $b=1$.
http://ijmc.kashanu.ac.ir/article_15385_09d45a56a3e6e888884635bfc073bf60.pdf
2017-03-01T11:23:20
2020-02-22T11:23:20
37
45
10.22052/ijmc.2017.15385
Bucket recursive trees
Multiplicative Zagreb index
Moment generating function
Moments
R.
Kazemi
r.kazemi@sci.ikiu.ac.ir
true
1
Imam Khomeini international university
Imam Khomeini international university
Imam Khomeini international university
LEAD_AUTHOR
1. P. Billingsley, Probability and Measure, John Wiley and Sons, New York, 1995.
1
2. M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative versions of first Zagreb index,
2
MATCH Commun. Math. Comput. Chem. 68 (2012), 217–230.
3
3. A. Iranmanesh, M. A. Hosseinzadeh, I. Gutman, On multiplicative Zagreb indices
4
of graphs, Iranian J. Math. Chem. 3 (2012), 145–154.
5
4. R. Kazemi, Probabilistic analysis of the first Zagreb index, Trans. Comb. 2 (2013),
6
35–40.
7
5. R. Kazemi, Depth in bucket recursive trees with variable capacities of buckets, Acta
8
Math. Sin. Engl. Ser. 30 (2014), 305–310.
9
6. R. Kazemi, The eccentric connectivity index of bucket recursive trees, Iranian J.
10
Math. Chem. 5 (2014), 77–83.
11
7. H. M. Mahmoud, R. T. Smythe, Probabilistic analysis of bucket recursive trees,
12
Theoret. Comput. Sci. 144 (1995), 221–249.
13
8. A. Meir, J. W. Moon, On the altitude of nodes in random trees, Canadian J. Math.
14
30 (1978), 997–1015.
15
9. R. Todeschini, D. Ballabio, V. Consonni, Novel molecular descriptors based on
16
functions of new vertex degrees, in: I. Gutman, B. Furtula (Eds.), Novel Molecular
17
Structure Descriptors Theory and Applications I, Univ. Kragujevac, Kragujevac
18
(2010), 73–100.
19
10. R. Todeschini, V. Consonni, New local vertex invariants and molecular descriptors
20
based on functions of the vertex degrees, MATCH Commun. Math. Comput. Chem.
21
64 (2010), 359–372.
22
ORIGINAL_ARTICLE
The Conditions of the Violations of Le Chatlier’s Principle in Gas Reactions at Constant T and P
Le Chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . However, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. In this article, we derived a simple equation for the violation of Le Chatelier's principle for the ideal gas reactions at the constant temperature and pressure.
http://ijmc.kashanu.ac.ir/article_40877_8ff2dc0bd3328b97fc4cc4983d8d533a.pdf
2017-03-01T11:23:20
2020-02-22T11:23:20
47
52
10.22052/ijmc.2016.40877
Violation of Le Chatelier
Principle gas reaction
Mixture
Chemical equilibria
Chemical potential moderation
M.
Torabi Rad
morteza.0mtr0@yahoo.com
true
1
University of Qom, Qom, Iran
University of Qom, Qom, Iran
University of Qom, Qom, Iran
AUTHOR
A.
Abbasi
a.abbasi@qom.ac.ir
true
2
University of Qom, Qom, Iran
University of Qom, Qom, Iran
University of Qom, Qom, Iran
LEAD_AUTHOR
1. H. Le Chatelier, Sur un énoncé général des lois des équilibres chimiques, Compt.
1
Rend. 99 (1884) 786–789.
2
2. D. Cheung, Using think-aloud protocols to investigate secondary school chemistry
3
teachers’ misconceptions about chemical equilibrium, Chem. Educ. Res. Pract. 10
4
(2009) 97–108.
5
3. D. Cheung, The Adverse Effects of Le Chatelier’s Principle on Teacher
6
Understanding of Chemical Equilibrium, J. Chem. Educ. 86 (2009) 514–518.
7
4. J. J.De Heer, The principle of Le Chatelier and Braun, Chem. Educ. 34 (1957)
8
375–380.
9
5. J. J. De Heer, Le Chatelier, scientific principle, or "sacred cow"?, Chem. Educ. 35
10
(1958) 133–136.
11
6. R. S. Treptow, Le Chatelier's principle: A reexamination and method of graphic
12
illustration, J. Chem. Educ. 57 (1980) 417–420.
13
7. J. Gold, V. Gold, Neither Le Chateliers nor a principle, Chem. Brit. 20 (1984)
14
802–806.
15
8. K. Posthumus, The application of the van't Hoff−le Chatelier−Braun principle to
16
chemical equilibria, Rec. Tray. Chim. 52 (1933) 25–35.
17
9. K. Posthumus, The application of the van't Hoff−le Chatelier−Braun principle to
18
chemical equilibria. II, Rec. Tray. Claim. 53 (1933) 308–311.
19
10. J. E. Lacy, Equilibria that shift left upon addition of more reactant, J. Chem. Educ.
20
82 (2005) 1192–1193.
21
ORIGINAL_ARTICLE
Neighbourly Irregular Derived Graphs
A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.
http://ijmc.kashanu.ac.ir/article_40878_84e728f990f1722c2fdf11f8aec1c6e0.pdf
2017-03-01T11:23:20
2020-02-22T11:23:20
53
60
10.22052/ijmc.2016.40878
Neighbourly irregular
Derived graphs
Product graphs
B.
Basavanagoud
b.basavanagoud@gmail.com
true
1
KARNATAK UNIVERSITY DHARWAD
KARNATAK UNIVERSITY DHARWAD
KARNATAK UNIVERSITY DHARWAD
LEAD_AUTHOR
S.
Patil
shreekantpatil949@gmail.com
true
2
Karnatak University
Karnatak University
Karnatak University
AUTHOR
V. R.
Desai
veenardesai6f@gmail.com
true
3
Karnatak University
Karnatak University
Karnatak University
AUTHOR
M.
Tavakoli
m_tavakoli@um.ac.ir
true
4
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
AUTHOR
A. R.
Ashrafi
ashrafi@kashanu.ac.ir
true
5
University of Kashan
University of Kashan
University of Kashan
AUTHOR
1. Y. Alavi, G. Chartrand, F. R. K. Chung, P. Erdos, H. L. Graham, O. R.
1
Oellermann, Highly irregular graphs, J. Graph Theory 11 (1987) 235–249.
2
2. S. G. Bhragsam, S. K. Ayyaswamy, Neighbourly irregular graphs, Indian J. Pure
3
Appl. Math. 35(3) (2004) 389–399.
4
3. T. Došlić, Vertex-weighted Wiener polynomials for composite graphs, Ars Math.
5
Contemp. 1 (2008) 66–80.
6
4. F. Harary, Graph Theory, Addison-Wesley Publishing Co. Inc., Reading, Mass.,
7
5. Y. Hou, W-C. Shiu, The spectrum of the edge corona of two graphs, Electron. J.
8
Linear Algebra 20 (2010) 586–594.
9
6. S. R. Jog, S. P. Hande, I. Gutman, S. B. Bozkurt, Derived graphs of some graphs,
10
Kragujevac J. Math. 36(2) (2012) 309–314.
11
7. V. R. Kulli, B. Basavanagoud, On the quasivertex-total graph of a graph, J.
12
Karnatak Uni. Sci. 42 (1998) 1–7.
13
8. E. Sampathkumar, S. B. Chikkodimath, Semitotal graphs of a graph-I, J.
14
Karnatak Uni. Sci. 18 (1973) 274–280.
15
9. D. V. S. Sastry, B. Syam Prasad Raju, Graph equations for line graphs, total
16
graphs, middle graphs and quasi-total graphs, Discrete Math. 48 (1984) 113–119.
17
10. M. Tavakoli, F. Rahbarnia, A. R. Ashrafi, Studying the corona product of graphs
18
under some graph invariants, Trans. Comb. 3(3) (2014) 43–49.
19
11. Y. N. Yeh, I. Gutman, On the sum of all distances in composite graphs, Discrete
20
Math. 135 (1994) 359–365.
21
12. H. B. Walikar, S. B. Halkarni, H. S. Ramane, M. Tavakoli, A. R. Ashrafi, On
22
neighbourly irregular graphs, Kragujevac J. Math. 39(1) (2015) 31–39.
23
ORIGINAL_ARTICLE
Splice Graphs and their Vertex-Degree-Based Invariants
Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.
http://ijmc.kashanu.ac.ir/article_42671_842a36edd0ad831bf464f22081c22654.pdf
2017-03-01T11:23:20
2020-02-22T11:23:20
61
70
10.22052/ijmc.2017.42671
vertex degree
graph invariant
Splice
M.
Azari
mahdie.azari@gmail.com
true
1
Islamic Azad University
Islamic Azad University
Islamic Azad University
LEAD_AUTHOR
F.
Falahati-Nezhad
farzanehfalahati_n@yahoo.com
true
2
Safadasht Branch, Islamic Azad University
Safadasht Branch, Islamic Azad University
Safadasht Branch, Islamic Azad University
AUTHOR
[1] M. V. Diudea, QSPR/QSAR Studies by Molecular Descriptors, New York, NOVA,
1
[2] I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer,
2
Berlin, 1986.
3
[3] N. Trinajstić, Chemical Graph Theory, CRC Press, Boca Raton, FL, 1992.
4
[4] M. Randić, On characterization of molecular branching, J. Am. Chem. Soc. 97 (1975)
5
6609–6615.
6
[5] B. Zhou and N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46 (2009)
7
1252–1270.
8
[6] S. Fajtlowicz, On conjectures on Graffiti–II, Congr. Numer. 60 (1987) 187–197.
9
[7] E. Estrada, L. Torres, L. Rodriguez and I. Gutman, An atom–bond connectivity index:
10
Modelling the enthalpy of formation of alkanes, Indian J. Chem. 37A (1998) 849–855.
11
[8] E. Estrada, Atom-bond connectivity and the energetic of branched alkanes, Chem.
12
Phys. Lett. 463 (2008) 422–425.
13
[9] B. Furtula, A. Graovac and D. Vukičević, Augmented Zagreb index, J. Math. Chem. 48
14
(2) (2010) 370–380.
15
[10] D. Vukičević and B. Furtula, Topological index based on the ratios of geometrical and
16
arithmetical means of end–vertex degrees of edges, J. Math. Chem. 46 (2009) 1369–1376.
17
[11] H. Deng, J. Yang and F. Xia, A general modeling of some vertex–degree based
18
topological indices in benzenoid systems and phenylenes, Comput. Math. Appl. 61 (2011)
19
3017–3023.
20
[12] A. R. Ashrafi, A. Hamzeh and S. Hossein–Zadeh, Calculation of some topological
21
indices of splices and links of graphs, J. Appl. Math. Inf. 29 (1–2) (2011) 327–335.
22
[13] M. Azari, Sharp lower bounds on the Narumi-Katayama index of graph operations,
23
Appl. Math. Comput. 239 C (2014) 409–421.
24
[14] M. Azari and A. Iranmanesh, Chemical graphs constructed from rooted product and
25
their Zagreb indices, MATCH Commun. Math. Comput. Chem. 70 (2013) 901–919.
26
[15] M. Azari and A. Iranmanesh, Computing the eccentric-distance sum for graph
27
operations, Discrete Appl. Math. 161 (18) (2013) 2827–2840.
28
[16] M. Azari and A. Iranmanesh, Computing Wiener–like topological invariants for some
29
composite graphs and some nanotubes and nanotori, In: I. Gutman, (Ed.), Topics in
30
Chemical Graph Theory, Univ. Kragujevac, Kragujevac, 2014, pp. 69–90.
31
[17] M. Azari, A. Iranmanesh and I. Gutman, Zagreb indices of bridge and chain graphs,
32
MATCH Commun. Math. Comput. Chem. 70 (2013) 921–938.
33
[18] A. Iranmanesh, M. A. Hosseinzadeh and I. Gutman, On multiplicative Zagreb indices
34
of graphs, Iranian J. Math. Chem. 3(2) (2012) 145–154.
35
[19] M. Mogharrab and I. Gutman, Bridge graphs and their topological indices, MATCH
36
Commun. Math. Comput. Chem. 69 (2013) 579–587.
37
[20] R. Sharafdini and I. Gutman, Splice graphs and their topological indices, Kragujevac
38
J. Sci. 35 (2013) 89–98.
39
[21] T. Došlić, Splices, links and their degree–weighted Wiener polynomials, Graph
40
Theory Notes New York 48 (2005) 47–55.
41
[22] M. Azari, A note on vertex–edge Wiener indices, Iranian J. Math. Chem. 7(1) (2016)
42
11–17.
43
ORIGINAL_ARTICLE
An Upper Bound on the First Zagreb Index in Trees
In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.
http://ijmc.kashanu.ac.ir/article_42995_aceaeaa2290cdaa2217a2205d4bda5af.pdf
2017-03-01T11:23:20
2020-02-22T11:23:20
71
82
10.22052/ijmc.2017.42995
First Zagreb index
First Zagreb coindex
tree
Chemical tree
R.
Rasi
true
1
Azarbaijan Shahid Madani University, Tabriz, Iran
Azarbaijan Shahid Madani University, Tabriz, Iran
Azarbaijan Shahid Madani University, Tabriz, Iran
AUTHOR
S.
Sheikholeslami
true
2
Azarbaijan Shahid Madani University, Tabriz, Iran
Azarbaijan Shahid Madani University, Tabriz, Iran
Azarbaijan Shahid Madani University, Tabriz, Iran
AUTHOR
A.
Behmaram
behmarammath@gmail.com
true
3
Institute for Research in Fundamental Sciences, Tehran, Iran
Institute for Research in Fundamental Sciences, Tehran, Iran
Institute for Research in Fundamental Sciences, Tehran, Iran
LEAD_AUTHOR
[1] A. R. Ashrafi, T. Došlić, A. Hamzeh, The Zagreb coindices of graph operations,
1
Discrete Appl. Math. 158 (2010), 1571–1578.
2
[2] K. C. Das, Sharp bounds for the sum of the squares of the degrees of a graph,
3
Kragujevac J. Math. 25 (2003), 31–49.
4
[3] K. C. Das, Maximizing the sum of the squares of the degrees of a graph, Discrete Math.
5
285 (2004), 57–66.
6
[4] D. de Caen, An upper bound on the sum of squares in a graph, Discrete Math. 185
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(1998), 245–248.
8
[5] T. Došlić, Vertex-weighted Wiener polynomials for composite graphs, Ars. Math.
9
Contemp. 1 (2008), 66–80.
10
[6] I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total -electron energy
11
of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535–538.
12
[7] X. L. Li, I. Gutman, Mathematical Aspects of Randić-Type Molecular Structure
13
Descriptors, Mathematical Chemistry Monograph 1, University of Kragujevac, 2006.
14
[8] S. Nikolić, G. Kovačević, A. Miličević, N. Trinajstić, The Zagreb indices 30 years after,
15
Croat. Chem. Acta 76 (2003), 113–124.
16
[9] Ž. Kovijanić Vukićević, G. Popivoda, Chemical trees with extreme values of Zagreb
17
indices and coindices, Iranian. J. Math. Chem. 5 (2014) 19–29.
18
[10] S. Zhang, W. Wang, T. C. E. Cheng, Bicyclic graphs with the first three smallest and
19
largest values of the first general Zagreb index, MATCH Commun. Math. Comput. Chem.
20
56 (2006), 579–592.
21
[11] B. Zhou, I. Gutman, Relations between Wiener, hyper-Wiener and Zagreb indices,
22
Chem. Phys. Lett. 394 (2004), 93–95.
23
ORIGINAL_ARTICLE
Distance-Based Topological Indices and Double graph
Let $G$ be a connected graph, and let $D[G]$ denote the double graph of $G$. In this paper, we first derive closed-form formulas for different distance based topological indices for $D[G]$ in terms of that of $G$. Finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topological indices.
http://ijmc.kashanu.ac.ir/article_43073_1e1bbd86540bb1e1baabd2a8f90bff47.pdf
2017-03-01T11:23:20
2020-02-22T11:23:20
83
91
10.22052/ijmc.2017.43073
Wiener index
Harary index
Double graph
M.
Jamil
m.kamran.sms@gmail.com
true
1
ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES, GOVERNMENT COLLEGE UNIVERSITY, LAHORE, PAKISTAN.
ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES, GOVERNMENT COLLEGE UNIVERSITY, LAHORE, PAKISTAN.
ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES, GOVERNMENT COLLEGE UNIVERSITY, LAHORE, PAKISTAN.
LEAD_AUTHOR
1. Y. Alizadeh, A. Iranmanesh, T. Dośolić, Additively weighted Harary index of
1
some composite graphs, Discrete Math. 313:1 (2013) 26–34.
2
2. M. V. Diudea, Indices of reciprocal properties or Harary indices, J. Chem. Inf.
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Comput. Sci. 37 (1997) 292–299.
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3. J. Devillers, A.T. Balaban (eds), Topological Indices and Related Descriptors in
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QSAR and QSPR, Gordon and Breach, Amsterdam, 1999.
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4. O. Ivanciuc, T. S. Balaban, Design of topological indices. Part 4. Reciprocal
7
distance matrix, related local vertex invariants and topological indices, J. Math.
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Chem. 12 (1993) 309–318.
9
5. A. Ilić, I. Gutman, Eccentric connectivity index of chemical trees, MATCH
10
Commun. Math. Comput. Chem. 65 (2011) 731–744.
11
6. E. Munarini, C. Perelli Cippo, A. Scagliola, N. Zagaglia Salvi, Double graphs,
12
Discrete Math. 308 (2008) 242–254.
13
7. D. Plav s ić, S. Nikolić, N. Trinajstić, Z. Mihalić, On the Harary index for the
14
characterization of chemical graphs, J. Math. Chem. 12 (1993) 235–250.
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8. M. Randić, On the characterization of molecular branching, J. Amer. Chem.
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Soc. 97 (1975) 6609–6615.
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9. V. Sharma, R. Goswami, A. K. Madan, Eccentric connectivity index: A novel
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highly discriminating topological descriptor for structure-property and structureactivity
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studies, J. Chem. Inf. Comput. Sci. 37 (1997) 273–282.
20
10. R. Todeschini, V. Consonni, Handbook of molecular descriptors, Wiley−VCH,
21
Weinheim, (2000) 209–212.
22
11. N. Trinajstić, S. Nikolić, S. C. Basak, I. Lukovits, Distance indices and their
23
hyper-counterparts: Intercorrelation and use in the structure-property modeling,
24
SAR QSAR Environ. Res. 12 (2001) 31–54.
25
12. D. B. West, Introduction to Graph Theory, Prentice-Hall, Upper Saddle River,
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13. H. Wiener, Structural determination of the paraffin points, J. Am. Chem. Soc.
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69 (1947) 17–20.
28