ORIGINAL_ARTICLE
Chebyshev finite difference method for a two−point boundary value problems with applications to chemical reactor theory
In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference scheme. The method is computationally attractive and applications are demonstrated through an illustrative example. Also a comparison is made with existing results.
https://ijmc.kashanu.ac.ir/article_5197_e39896886e9c361a7e56fda0b7f221a5.pdf
2012-02-01T11:23:20
2020-08-12T11:23:20
1
7
10.22052/ijmc.2012.5197
Chemical reactor
Chebyshev finite difference method
Numerical methods
Boundary value problems
Gauss–Lobatto nodes
A.
Saadatmandi
saadatmandi@kashanu.ac.ir
true
1
University of Kashan
University of Kashan
University of Kashan
LEAD_AUTHOR
M.
Azizi
true
2
Shariaty Technical College
Shariaty Technical College
Shariaty Technical College
AUTHOR
ORIGINAL_ARTICLE
Study of fullerenes by their algebraic properties
The eigenvalues of a graph is the root of its characteristic polynomial. A fullerene F is a 3- connected graphs with entirely 12 pentagonal faces and n/2 -10 hexagonal faces, where n is the number of vertices of F. In this paper we investigate the eigenvalues of a class of fullerene graphs.
https://ijmc.kashanu.ac.ir/article_5198_a8fa41f6fd14aa9bd445b3b2f8726e3b.pdf
2012-02-01T11:23:20
2020-08-12T11:23:20
9
24
10.22052/ijmc.2012.5198
Molecular Graph
Adjacency matrix
Eigenvalue
Fullerene
M.
Ghorbani
ghorbani30@gmail.com
true
1
Shahid Rajaee Teacher Training
University
Shahid Rajaee Teacher Training
University
Shahid Rajaee Teacher Training
University
LEAD_AUTHOR
S.
Heidari Rad
true
2
Shahid Rajaee Teacher Training
University
Shahid Rajaee Teacher Training
University
Shahid Rajaee Teacher Training
University
AUTHOR
1. I. Gutman, The energy of a graph, Ber. Math.Statist. Sekt. Forsch. Graz 103 (1978) 1–
1
2. I. Gutman, The Energy of a Graph: Old and New Results, Algebraic Combinatorics and
2
Applications, SpringerVerlag, Berlin, 2001.
3
3. I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry,
4
SpringerVerlag, Berlin, 1986.
5
4. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl and R. E. Smalley, C60:
6
Buckminsterfullerene. Nature 318 (1985) 162–163.
7
5. H. W. Kroto, J. E. Fichier and D. E. Cox, The Fullerene, Pergamon Press, New York,
8
6. D. Cvetković, M. Doob and H. Sachs, Spectra of Graphs: Theory and Applications (Pure
9
and Applied Mathematics), Academic Press, 1997.
10
7. S. L. Lee, Y. L. Luo, B. E. Sagan and Y.-N. Yeh, Eigenvectors and eigenvalues of some
11
special graphs, IV multilevel circulants. Int. J. Quant. Chem. 41 (1992) 105 – 116.
12
ORIGINAL_ARTICLE
On discriminativity of Zagreb indices
Zagreb indices belong to better known and better researched topological indices. We investigate here their ability to discriminate among benzenoid graphs and arrive at some quite unexpected conclusions. Along the way we establish tight (and sometimes sharp) lower and upper bounds on various classes of benzenoids.
https://ijmc.kashanu.ac.ir/article_5199_c6ae7c7fcc36f66e8bee02e54e98d61a.pdf
2012-02-01T11:23:20
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25
34
10.22052/ijmc.2012.5199
Zagreb index
Benzenoid graph
Catacondensed benzenoid
T.
Doslic
doslic@master.grad.hr
true
1
University of Zagreb
University of Zagreb
University of Zagreb
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. J. Braun, A. Kerber, M. Meringer, C. Rucker, Similarity of molecular descriptors:
3
the equivalence of Zagreb indices and walk counts, MATCH Commun. Math.
4
Comput. Chem. 54 (2005), 163–176.
5
3. D. de Caen, An upper bound on the sum of squares of degrees in a graph, Discrete
6
Math. 185 (1998) 245–248.
7
4. S. J. Cyvin, I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons, Lec. Notes
8
in Chemistry, Springer, Heidelberg, 1988.
9
5. K. Ch. Das, Maximizing the sum of the squares of the degrees of a graph, Discrete
10
Math. 285 (2004) 57–66.
11
6. K. Ch. Das, I. Gutman, Some properties of the second Zagreb index, MATCH
12
Commun. Math. Comput. Chem. 52 (2004) 103–112.
13
7. T. Došlić, Vertex-Weighted Wiener Polynomials for Composite Graphs, Ars Math.
14
Contemp. 1 (2008) 66–80.
15
8. I. Gutman, K. Ch. Das, The first Zagreb index 30 years after, MATCH Commun.
16
Math. Comput. Chem. 50 (2004) 83–92.
17
9. M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, The first and second Zagreb
18
indices of graph operations, Discrete Appl. Math. 157 (2009) 804–811.
19
10. M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, S.Wagner, Some new results on
20
distance-based graph invariants, Europ. J. Combin. 30 (2009) 1149–1163.
21
11. D. J. Klein, T. Došlić, D. Bonchev, Vertex-weightings for distance moments and
22
thorny graphs, Discrete Appl. Math. 155 (2007) 2294–2302.
23
12. V. Nikiforov, The sum of the squares of degrees: an overdue assignment,
24
arXiv:math/0608660.
25
13. S. Nikolić, G. Kovačević, A. Miličević, N. Trinajstić, The Zagreb Indices 30 Years
26
After, Croat. Chem. Acta 76 (2003) 113–124.
27
14. D. B. West, Introduction to Graph Theory, Prentice Hall, Upper Saddle River,
28
15. S. Yamaguchi, Estimating the Zagreb indices and the spectral radius of triangle-and
29
quadrangle-free connected graphs, Chem. Phys. Lett. 458 (2008) 396–398.
30
16. Y. S. Yoon, J. K. Kim, A relationship between bounds on the sum of squares of
31
degrees of graph, J. Appl. Math. & Comput. 21 (2006) 233–238.
32
17. B. Zhou, I. Gutman, Relations between Wiener, hyper-Wiener and Zagreb indices,
33
Chem. Phys. Lett. 394 (2004) 93–95.
34
18. B. Zhou, Upper bounds for the Zagreb indices and the spectral radius of seriesparallel
35
graphs, Int. J. Quant. Chem. 107 (2007) 875–878.
36
19. B. Zhou, N. Trinajstić, On reciprocal molecular topological index, J. Math. Chem.
37
44 (2008) 235–243.
38
ORIGINAL_ARTICLE
Centric connectivity index by shell matrices
Relative centricity RC values of vertices/atoms are calculated within the Distance Detour and Cluj-Distance criteria on their corresponding Shell transforms. The vertex RC distribution in a molecular graph gives atom equivalence classes, useful in interpretation of NMR spectra. Timed by vertex valences, RC provides a new index, called Centric Connectivity CC, which can be useful in the topological characterization of graphs and in QSAR/QSPR studies.
https://ijmc.kashanu.ac.ir/article_5200_d41d8cd98f00b204e9800998ecf8427e.pdf
2012-02-01T11:23:20
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35
43
10.22052/ijmc.2012.5200
Graph theory
Cluj matrix
Relative centricity
Centric connectivity index
M.
Diudea
diudea@gmail.com
true
1
Babes-Bolyai University
Babes-Bolyai University
Babes-Bolyai University
AUTHOR
1. N. Trinajstić, Chemical Graph Theory, CRC Press: Boca Raton, FL, 1983.
1
2. F. Harary, Graph Theory, Addison-Wesley, Reading, M.A., 1969.
2
3. M. V. Diudea, I. Gutman, and L. Janschi, Molecular Topology, Nova Science,
3
Huntington, N. Y., 2001.
4
4. M. V. Diudea, Nanomolecules and Nanostructures, Polynomials and Indices, MCM,
5
No. 10, Univ. Kragujevac and Fac. Sci. Kragujevac, Serbia, 2010.
6
5. M. V. Diudea, M. S. Florescu, and P. V. Khadikar, Molecular Topology and Its
7
Applications, EFICON, Bucharest, 2006.
8
6. H. Wiener, Structural Determination of Paraffin Boiling points, J.Am.Chem.Soc.
9
1947, 69, 17-20.
10
7. I. Lukovits, The Detour Index, Croat. Chem. Acta, 1996, 69, 873-882.
11
8. I. Lukovits and M. Razinger, On Calculation of the Detour Index,
12
J. Chem. Inf. Comput. Sci., 1997, 37, 283-286.
13
9. M. V. Diudea, Cluj Matrix Invariants. J. Chem. Inf. Comput. Sci. 1997, 37, 300-
14
10. M. V. Diudea, Cluj Matrix CJu: source of various graph descriptors, Commun.
15
Math. Comput. Chem. (MATCH), 1997, 35, 169-183.
16
11. M. V. Diudea and I. Gutman, Wiener-Type Topological Indices. Croat. Chem. Acta,
17
1998, 71, 21-51.
18
12. M. V. Diudea, Valencies of Property. Croat. Chem. Acta, 1999, 72, 835-851.
19
13. M. V. Diudea, B. Parv, and I. Gutman, Detour-Cluj Matrix and Derived Invariants
20
J. Chem. Inf. Comput. Sci. 1997, 37, 1101-1108.
21
14. C. Y. Hu and L. Xu, Algorithm for Computer Perception of Topological Symmetry.
22
Anal. Chim. Acta, 1994, 295, 127-134.
23
15. G. S. Ezra, Symmetry Properties of Molecules, Lecture Notes in Chemistry 28,
24
Springer, 1982.
25
16. M. Razinger, K. Balasubramanian, and M. E. Munk, Graph Automorphism
26
Perception Algorithms in Computer-Enhanced Structure Elucidation. J. Chem. Inf.
27
Comput. Sci., 1993, 33, 197-201.
28
17. Bonchev, D.; Balaban, A.T.; Randić, M. The Graph Center Concept for Polycyclic
29
Graphs, Int. J. Quantum Chem. 1981, 19, 61-82.
30
18. Bonchev, D.; Mekenyan, O.; Balaban, A.T. Iterative Procedure for the Generalized
31
Graph Center in Polycyclic Graphs, J. Chem. Inf. Comput. Sci. 1989, 29, 91-97.
32
19. M. V. Diudea, Layer Matrices in Molecular Graphs, J. Chem. Inf. Comput. Sci.
33
1994, 34, 1064-1071.
34
20. M. V. Diudea, M. Topan, and A. Graovac, Layer Matrices of Walk Degrees, J.
35
Chem. Inf. Comput. Sci. 1994, 34, 1071 -1078.
36
21. M. V. Diudea and O. Ursu, Layer matrices and distance property descriptors.
37
Indian J. Chem., 42A, 2003, 1283-1294.
38
22. V. Sharma, R. Goswami, A. K. Madan, Eccentric connectivity index: A novel
39
highly discriminating topological descriptor for structure property and structure
40
activity studies, J. Chem. Inf. Comput. Sci. 37 (1997) 273-282.
41
23. P. E. John and M. V. Diudea, The second distance matrix of the graph and its
42
characteristic polynomial, Carpath. J. Math., 2004, 20 (2), 235-239.
43
24. T. Balaban, O. Mekenyan, and D. Bonchev, Unique Description of Chemical
44
Structures Based on Hierarchically Ordered Extended Connectivities (HOC
45
Procedures). I. Algorithms for Finding graph Orbits and Cannonical Numbering of
46
Atoms, J. Comput. Chem. 1985, 6, 538-551.
47
25. A. T. Balaban, O. Mekenyan, and D. Bonchev, Unique Description of Chemical
48
Structures Based on Hierarchically Ordered Extended Connectivities (HOC
49
Procedures). II. Mathematical Proofs for the HOC Algorithm, J. Comput. Chem.
50
1985, 6, 552-561.
51
26. O. Mekenyan, A. T. Balaban, and D. Bonchev, Unique Description of Chemical
52
Structures Based on Hierarchically Ordered Extended Connectivities (HOC
53
Procedures). VI. Condensed Benzenoid Hydrocarbons and Their 1H-NMR
54
Chemical Shifts. J. Magn. Reson. 1985, 63, 1-13.
55
27. A.T. Balaban, A. T.; Moţoc, I.; Bonchev, D.; Mekenyan, O. Topological Indices for
56
Structure - Activity Correlations, Top. Curr. Chem. 1993, 114, 21-55.
57
28. H Morgan, The generation of a unique machine description for chemical structures.
58
A technique developed at Chemical Abstracts Service, J. Chem. Doc. 1965, 5, 107-
59
29. A. Ilić, I. Gutman, Eccentric Connectivity Index of Chemical Trees, MATCH
60
Commun. Math. Comput. Chem. 65 (2011), 731-744.
61
30. A. Ilić, Eccentric connectivity index, in: I. Gutman, B. Furtula, Novel Molecular
62
Structure Descriptors -Theory and Applications II, MCM 9, University of
63
Kragujevac, 2010.
64
31. G. Yu, L. Feng, A. Ilić, On the eccentric distance sum of trees and unicyclic graphs,
65
J. Math. Anal. Appl. 375 (2011), 934-944.
66
32. M. V. Diudea, Centric connectivity index, Studia Univ. Babes-Bolyai, Chemia,
67
2010, 55 (4), 319-324.
68
ORIGINAL_ARTICLE
Distance-based topological indices of tensor product of graphs
Let G and H be connected graphs. The tensor product G + H is a graph with vertex set V(G+H) = V (G) X V(H) and edge set E(G + H) ={(a , b)(x , y)| ax ∈ E(G) & by ∈ E(H)}. The graph H is called the strongly triangular if for every vertex u and v there exists a vertex w adjacent to both of them. In this article the tensor product of G + H under some distancebased topological indices are investigated, when H is a strongly triangular graph. As a special case most of results given by Hoji, Luob and Vumara in [Wiener and vertex PI indices of Kronecker products of graphs, Discrete Appl. Math., 158 (2010), 1848-1855] will be deduced.
https://ijmc.kashanu.ac.ir/article_5201_d41d8cd98f00b204e9800998ecf8427e.pdf
2012-02-01T11:23:20
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45
53
10.22052/ijmc.2012.5201
tensor product
Wiener type invariant
Strongly triangular graph
M.
Nadjafi-Arani
mjnajafiarani@gmail.com
true
1
University of Kashan
University of Kashan
University of Kashan
AUTHOR
H.
Khodashenas
khodashenas@kashanu.ac.ir
true
2
University of Kashan
University of Kashan
University of Kashan
AUTHOR
ORIGINAL_ARTICLE
On the edge reverse Wiener indices of TUC4C8(S) nanotubes
The edge versions of reverse Wiener indices were introduced by Mahmiani et al. very recently. In this paper, we find their relation with ordinary (vertex) Wiener index in some graphs. Also, we compute them for trees and TUC4C8(s) naotubes.
https://ijmc.kashanu.ac.ir/article_5209_2f3c005d91db72be764cbb2f564ab33e.pdf
2012-02-01T11:23:20
2020-08-12T11:23:20
55
65
10.22052/ijmc.2012.5209
Molecular Graph
Molecular matrix
Reveres Wiener indices
Edge reverse
Wiener indices
Distance of graph
line graph
Nanotubes
A.
Mahmiani
true
1
Payame Noor University
Payame Noor University
Payame Noor University
AUTHOR
O.
Khormali
true
2
Tarbiat Modares University
Tarbiat Modares University
Tarbiat Modares University
AUTHOR
A.
Iranmanesh
iranmanesh@modares.ac.i
true
3
Tarbiat Modares University
Tarbiat Modares University
Tarbiat Modares University
LEAD_AUTHOR
ORIGINAL_ARTICLE
Computing the Szeged index of 4,4 ׳-bipyridinium dendrimer
Let e be an edge of a G connecting the vertices u and v. Define two sets N1 (e | G) and N2(e |G) as N1(e | G)= {xV(G) d(x,u) d(x,v)} and N2(e | G)= {xV(G) d(x,v) d(x,u) }.The number of elements of N1(e | G) and N2(e | G) are denoted by n1(e | G) and n2(e | G) , respectively. The Szeged index of the graph G is defined as Sz(G) ( ) ( ) 1 2 n e G n e G e E . In this paper we compute the Szeged index of a 4,4 ׳-Bipyridinium dendrimer.
https://ijmc.kashanu.ac.ir/article_5219_15c1f93cb85459d4528af627573c4871.pdf
2012-02-01T11:23:20
2020-08-12T11:23:20
67
72
10.22052/ijmc.2012.5219
Molecular Graph
Dendrimer
Szeged index
4
4 ׳-Bipyridinium
A.
ARJOMANFAR
true
1
Shar-e-Ray Branch,Iran
Shar-e-Ray Branch,Iran
Shar-e-Ray Branch,Iran
AUTHOR
N.
GHOLAMI
true
2
Islamic Azad University, Izeh Branch, Khouzestan, Iran
Islamic Azad University, Izeh Branch, Khouzestan, Iran
Islamic Azad University, Izeh Branch, Khouzestan, Iran
AUTHOR
ORIGINAL_ARTICLE
Some topological indices of graphs and some inequalities
Let G be a graph. In this paper, we study the eccentric connectivity index, the new version of the second Zagreb index and the forth geometric–arithmetic index.. The basic properties of these novel graph descriptors and some inequalities for them are established.
https://ijmc.kashanu.ac.ir/article_5220_4344681665ed2139c3c285378453c9ad.pdf
2012-02-01T11:23:20
2020-08-12T11:23:20
73
80
10.22052/ijmc.2012.5220
topological index
Eccentric connectivity
Geometric–arithmetic
Zagreb index
Cauchy–Schwarz inequality
M.
MOGHARRAB
true
1
Persian Gulf University, Bushehr, Iran
Persian Gulf University, Bushehr, Iran
Persian Gulf University, Bushehr, Iran
AUTHOR
B.
KHEZRI–MOGHADDAM
true
2
Payame Noor University, Shiraz,
Iran
Payame Noor University, Shiraz,
Iran
Payame Noor University, Shiraz,
Iran
AUTHOR
ORIGINAL_ARTICLE
Automatic graph construction of periodic open tubulene ((5,6,7)3) and computation of its Wiener, PI, and Szeged indices
The mathematical properties of nano molecules are an interesting branch of nanoscience for researches nowadays. The periodic open single wall tubulene is one of the nano molecules which is built up from two caps and a distancing nanotube/neck. We discuss how to automatically construct the graph of this molecule and plot the graph by spring layout algorithm in graphviz and netwrokx packages. The similarity between the shape of this molecule and the plotted graph is a consequence of our work. Furthermore, the Wiener, Szeged and PI indices of this molecule are computed.
https://ijmc.kashanu.ac.ir/article_5221_7e3ced6b5d005ed92da509c1085bd32a.pdf
2012-02-01T11:23:20
2020-08-12T11:23:20
81
94
10.22052/ijmc.2012.5221
Open tubulene
topological index
Szeged index
Wiener index
PI index
A.
YOOSOFAN
true
1
University of Kashan,
Iran
University of Kashan,
Iran
University of Kashan,
Iran
AUTHOR
M.
NAMAZI−FARD
true
2
University of Kashan,
Iran
University of Kashan,
Iran
University of Kashan,
Iran
AUTHOR