ORIGINAL_ARTICLE
Note on Properties of First Zagreb Index of Graphs
Let G be a graph. The first Zagreb M1(G) of graph G is defined as: M1(G) = uV(G) deg(u)2. In this paper, we prove that each even number except 4 and 8 is a first Zagreb index of a caterpillar. Also, we show that the fist Zagreb index cannot be an odd number. Moreover, we obtain the fist Zagreb index of some graph operations.
http://ijmc.kashanu.ac.ir/article_5269_88e60cb49fa19ed72edeae0db9befde3.pdf
2012-12-01T11:23:20
2020-02-22T11:23:20
1
5
10.22052/ijmc.2012.5269
Topological indices
The first and second Zagreb indices
tree
Graph operation
Strongly distance-balanced graph
M.
TAVAKOLI
true
1
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
AUTHOR
F.
RAHBARNIA
true
2
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
AUTHOR
ORIGINAL_ARTICLE
Eccentric Connectivity Index of Some Dendrimer Graphs
The eccentricity connectivity index of a molecular graph G is defined as (G) = aV(G) deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to other vertices of G and deg(a) is degree of vertex a. Here, we compute this topological index for some infinite classes of dendrimer graphs.
http://ijmc.kashanu.ac.ir/article_5270_22121ef8fc11a8b1d9590fd604033097.pdf
2012-12-01T11:23:20
2020-02-22T11:23:20
7
18
10.22052/ijmc.2012.5270
Eccentricity
topological index
Dendrimer graphs
M.
GHORBANI
true
1
Shahid Rajaee Teacher Training
University, I. R. Iran;
Shahid Rajaee Teacher Training
University, I. R. Iran;
Shahid Rajaee Teacher Training
University, I. R. Iran;
AUTHOR
KH.
MALEKJANI
true
2
Shahid Rajaee Teacher Training
University, I. R. Iran;
Shahid Rajaee Teacher Training
University, I. R. Iran;
Shahid Rajaee Teacher Training
University, I. R. Iran;
AUTHOR
A.
KHAKI
true
3
Shahid Rajaee Teacher Training
University, I. R. Iran;
Shahid Rajaee Teacher Training
University, I. R. Iran;
Shahid Rajaee Teacher Training
University, I. R. Iran;
AUTHOR
ORIGINAL_ARTICLE
Computing GA4 Index of Some Graph Operations
The geometric-arithmetic index is another topological index was defined as 2 deg ( )deg ( ) ( ) deg ( ) deg ( ) G G uv E G G u v GA G u v , in which degree of vertex u denoted by degG (u). We now define a new version of GA index as 4 ( ) 2 ε ( )ε ( ) ( ) ε ( ) ε ( ) G G e uv E G G G u v GA G u v , where εG(u) is the eccentricity of vertex u. In this paper we compute this new topological index for two graph operations.
http://ijmc.kashanu.ac.ir/article_5271_e45e1b12bd7d45ac826b874c26ef0661.pdf
2012-12-01T11:23:20
2020-02-22T11:23:20
19
28
10.22052/ijmc.2012.5271
topological index
GA Index
GA_{4} index
Graph operations
M.
SAHELI
true
1
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
AUTHOR
M.
JALALI RAD
true
2
University of Kashan,
Kashan, I. R. Iran
University of Kashan,
Kashan, I. R. Iran
University of Kashan,
Kashan, I. R. Iran
AUTHOR
ORIGINAL_ARTICLE
On Symmetry of Some Nano Structures
It is necessary to generate the automorphism group of a chemical graph in computer-aided structure elucidation. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. A.T. Balaban introduced some monster graphs and then M. Randic computed complexity indices of them (see A.T. Balaban, Rev. Roum. Chim. 18(1973) 841-853 and M. Randic, Croat. Chem. Acta 74(3)(2001) 683- 705). In this paper, we describe a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs.
http://ijmc.kashanu.ac.ir/article_5272_4354587496110c6a075b0d1990485b94.pdf
2012-12-01T11:23:20
2020-02-22T11:23:20
29
36
10.22052/ijmc.2012.5272
Weighted graph
Euclidean graph
M.
GHORBANI
true
1
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
AUTHOR
A.
ZAEEMBASHI
true
2
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
AUTHOR
M.
SHAHREZAEI
true
3
Imam Hossein University,
I.R. Iran
Imam Hossein University,
I.R. Iran
Imam Hossein University,
I.R. Iran
AUTHOR
A.
TABATABAEI ADNANI
true
4
Islamic Azad University, I. R. Iran
Islamic Azad University, I. R. Iran
Islamic Azad University, I. R. Iran
AUTHOR
ORIGINAL_ARTICLE
Applications of Graph Operations
In this paper, some applications of our earlier results in working with chemical graphs are presented.
http://ijmc.kashanu.ac.ir/article_5273_84937ba7dd780549b008d14ef626f331.pdf
2012-12-01T11:23:20
2020-02-22T11:23:20
37
43
10.22052/ijmc.2012.5273
topological index
Graph operation
Hierarchical product
Chemical graph
M.
TAVAKOLI
true
1
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
AUTHOR
F.
RAHBARNIA
true
2
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
AUTHOR
ORIGINAL_ARTICLE
Geometric-Arithmetic Index of Hamiltonian Fullerenes
A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.
http://ijmc.kashanu.ac.ir/article_5274_132874a2fbc48fc20a2cd83418227b21.pdf
2012-12-01T11:23:20
2020-02-22T11:23:20
45
50
10.22052/ijmc.2012.5274
Fullerene graphs
Hamiltonian graphs
Geometric –arithmetic index
H.
MOSTAFAEI
true
1
Islamic Azad University, Tehran, Iran
Islamic Azad University, Tehran, Iran
Islamic Azad University, Tehran, Iran
AUTHOR
A.
ZAEEMBASHI
true
2
Shahid Rajaee Teacher Training
University, Tehran, I. R. Iran
Shahid Rajaee Teacher Training
University, Tehran, I. R. Iran
Shahid Rajaee Teacher Training
University, Tehran, I. R. Iran
AUTHOR
M.
OSTAD RAHIMI
true
3
Tehran North Branch, Islamic Azad University,
Iran
Tehran North Branch, Islamic Azad University,
Iran
Tehran North Branch, Islamic Azad University,
Iran
AUTHOR
ORIGINAL_ARTICLE
On Counting Polynomials of Some Nanostructures
The Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.
http://ijmc.kashanu.ac.ir/article_5275_598bbbb545b1a47f060eba52713bf436.pdf
2012-12-01T11:23:20
2020-02-22T11:23:20
51
58
10.22052/ijmc.2012.5275
Omega polynomial
PI polynomial
Nanostar dendrimers
M.
GHORBANI
true
1
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
AUTHOR
M.
SONGHORI
true
2
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
AUTHOR
ORIGINAL_ARTICLE
Computing Chemical Properties of Molecules by Graphs and Rank Polynomials
The topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The Tutte polynomial of is a polynomial in two variables defined for every undirected graph contains information about connectivity of the graph. The Padmakar-Ivan, vertex Padmakar-Ivan polynomials of a graph are polynomials in one variable defined for every simple connected graphs that are undirected. In this paper, we compute these polynomials of two infinite classes of dendrimer nanostars.
http://ijmc.kashanu.ac.ir/article_5276_79a271992b7bcfde9d597fe6eba83405.pdf
2012-12-01T11:23:20
2020-02-22T11:23:20
59
65
10.22052/ijmc.2012.5276
Dendrimers
Tutte polynomial
PI-polynomial
M.
MOGHARRAB
true
1
Persian Gulf University,
I.R. Iran
Persian Gulf University,
I.R. Iran
Persian Gulf University,
I.R. Iran
AUTHOR
G.
FATH-TABAR
true
2
University of
Kashan, I. R. Iran
University of
Kashan, I. R. Iran
University of
Kashan, I. R. Iran
AUTHOR
ORIGINAL_ARTICLE
A Note on Atom Bond Connectivity Index
The atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G) uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.
http://ijmc.kashanu.ac.ir/article_5277_d209553fa79f35c61cae445c78d6baa4.pdf
2012-12-01T11:23:20
2020-02-22T11:23:20
67
75
10.22052/ijmc.2012.5277
topological index
ABC Index
Nanotube
Nanotori
S.
HEIDARI RAD
true
1
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
AUTHOR
A.
KHAKI
true
2
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University, I. R. Iran
AUTHOR