University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
Supplement 1
2012
12
01
Note on Properties of First Zagreb Index of Graphs
1
5
EN
M.
TAVAKOLI
Ferdowsi University of Mashhad, Iran
F.
RAHBARNIA
Ferdowsi University of Mashhad, Iran
10.22052/ijmc.2012.5269
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.
Topological indices,The first and second Zagreb indices,Tree,Graph operation,Strongly distance-balanced graph
http://ijmc.kashanu.ac.ir/article_5269.html
http://ijmc.kashanu.ac.ir/article_5269_88e60cb49fa19ed72edeae0db9befde3.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
Supplement 1
2012
12
01
Eccentric Connectivity Index of Some Dendrimer Graphs
7
18
EN
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran;
KH.
MALEKJANI
Shahid Rajaee Teacher Training
University, I. R. Iran;
A.
KHAKI
Shahid Rajaee Teacher Training
University, I. R. Iran;
10.22052/ijmc.2012.5270
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.
Eccentricity,Topological index,Dendrimer graphs
http://ijmc.kashanu.ac.ir/article_5270.html
http://ijmc.kashanu.ac.ir/article_5270_22121ef8fc11a8b1d9590fd604033097.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
Supplement 1
2012
12
01
Computing GA4 Index of Some Graph Operations
19
28
EN
M.
SAHELI
University of Kashan, I. R. Iran
M.
JALALI RAD
University of Kashan,
Kashan, I. R. Iran
10.22052/ijmc.2012.5271
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.
Topological index,GA Index,GA_{4} index,Graph operations
http://ijmc.kashanu.ac.ir/article_5271.html
http://ijmc.kashanu.ac.ir/article_5271_e45e1b12bd7d45ac826b874c26ef0661.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
Supplement 1
2012
12
01
On Symmetry of Some Nano Structures
29
36
EN
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
A.
ZAEEMBASHI
Shahid Rajaee Teacher Training
University, I. R. Iran
M.
SHAHREZAEI
Imam Hossein University,
I.R. Iran
A.
TABATABAEI ADNANI
Islamic Azad University, I. R. Iran
10.22052/ijmc.2012.5272
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.
Weighted graph,Euclidean graph
http://ijmc.kashanu.ac.ir/article_5272.html
http://ijmc.kashanu.ac.ir/article_5272_4354587496110c6a075b0d1990485b94.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
Supplement 1
2012
12
01
Applications of Graph Operations
37
43
EN
M.
TAVAKOLI
Ferdowsi University of Mashhad, Iran
F.
RAHBARNIA
Ferdowsi University of Mashhad, Iran
10.22052/ijmc.2012.5273
In this paper, some applications of our earlier results in working with chemical graphs are presented.
Topological index,Graph operation,Hierarchical product,Chemical graph
http://ijmc.kashanu.ac.ir/article_5273.html
http://ijmc.kashanu.ac.ir/article_5273_84937ba7dd780549b008d14ef626f331.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
Supplement 1
2012
12
01
Geometric-Arithmetic Index of Hamiltonian Fullerenes
45
50
EN
H.
R.
MOSTAFAEI
Islamic Azad University, Tehran, Iran
A.
ZAEEMBASHI
Shahid Rajaee Teacher Training
University, Tehran, I. R. Iran
M.
OSTAD RAHIMI
Tehran North Branch, Islamic Azad University,
Iran
10.22052/ijmc.2012.5274
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.
Fullerene graphs,Hamiltonian graphs,Geometric –arithmetic index
http://ijmc.kashanu.ac.ir/article_5274.html
http://ijmc.kashanu.ac.ir/article_5274_132874a2fbc48fc20a2cd83418227b21.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
Supplement 1
2012
12
01
On Counting Polynomials of Some Nanostructures
51
58
EN
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
M.
SONGHORI
Shahid Rajaee Teacher Training
University, I. R. Iran
10.22052/ijmc.2012.5275
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.
Omega polynomial,PI polynomial,Nanostar dendrimers
http://ijmc.kashanu.ac.ir/article_5275.html
http://ijmc.kashanu.ac.ir/article_5275_598bbbb545b1a47f060eba52713bf436.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
Supplement 1
2012
12
01
Computing Chemical Properties of Molecules by Graphs and Rank Polynomials
59
65
EN
M.
MOGHARRAB
Persian Gulf University,
I.R. Iran
G.
H.
FATH-TABAR
University of
Kashan, I. R. Iran
10.22052/ijmc.2012.5276
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.
Dendrimers,Tutte polynomial,PI-polynomial
http://ijmc.kashanu.ac.ir/article_5276.html
http://ijmc.kashanu.ac.ir/article_5276_79a271992b7bcfde9d597fe6eba83405.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
3
Supplement 1
2012
12
01
A Note on Atom Bond Connectivity Index
67
75
EN
S.
HEIDARI RAD
Shahid Rajaee Teacher Training
University, I. R. Iran
A.
KHAKI
Shahid Rajaee Teacher Training
University, I. R. Iran
10.22052/ijmc.2012.5277
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.
Topological index,ABC Index,Nanotube,Nanotori
http://ijmc.kashanu.ac.ir/article_5277.html
http://ijmc.kashanu.ac.ir/article_5277_d209553fa79f35c61cae445c78d6baa4.pdf