Note on Properties of First Zagreb Index of Graphs
M.
TAVAKOLI
Ferdowsi University of Mashhad, Iran
author
F.
RAHBARNIA
Ferdowsi University of Mashhad, Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
Supplement 1
no.
2012
1
5
http://ijmc.kashanu.ac.ir/article_5269_88e60cb49fa19ed72edeae0db9befde3.pdf
dx.doi.org/10.22052/ijmc.2012.5269
Eccentric Connectivity Index of Some Dendrimer Graphs
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran;
author
KH.
MALEKJANI
Shahid Rajaee Teacher Training
University, I. R. Iran;
author
A.
KHAKI
Shahid Rajaee Teacher Training
University, I. R. Iran;
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
Supplement 1
no.
2012
7
18
http://ijmc.kashanu.ac.ir/article_5270_22121ef8fc11a8b1d9590fd604033097.pdf
dx.doi.org/10.22052/ijmc.2012.5270
Computing GA4 Index of Some Graph Operations
M.
SAHELI
University of Kashan, I. R. Iran
author
M.
JALALI RAD
University of Kashan,
Kashan, I. R. Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
Supplement 1
no.
2012
19
28
http://ijmc.kashanu.ac.ir/article_5271_e45e1b12bd7d45ac826b874c26ef0661.pdf
dx.doi.org/10.22052/ijmc.2012.5271
On Symmetry of Some Nano Structures
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
A.
ZAEEMBASHI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
M.
SHAHREZAEI
Imam Hossein University,
I.R. Iran
author
A.
TABATABAEI ADNANI
Islamic Azad University, I. R. Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
Supplement 1
no.
2012
29
36
http://ijmc.kashanu.ac.ir/article_5272_4354587496110c6a075b0d1990485b94.pdf
dx.doi.org/10.22052/ijmc.2012.5272
Applications of Graph Operations
M.
TAVAKOLI
Ferdowsi University of Mashhad, Iran
author
F.
RAHBARNIA
Ferdowsi University of Mashhad, Iran
author
text
article
2012
eng
In this paper, some applications of our earlier results in working with chemical graphs are presented.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
Supplement 1
no.
2012
37
43
http://ijmc.kashanu.ac.ir/article_5273_84937ba7dd780549b008d14ef626f331.pdf
dx.doi.org/10.22052/ijmc.2012.5273
Geometric-Arithmetic Index of Hamiltonian Fullerenes
H.
MOSTAFAEI
Islamic Azad University, Tehran, Iran
author
A.
ZAEEMBASHI
Shahid Rajaee Teacher Training
University, Tehran, I. R. Iran
author
M.
OSTAD RAHIMI
Tehran North Branch, Islamic Azad University,
Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
Supplement 1
no.
2012
45
50
http://ijmc.kashanu.ac.ir/article_5274_132874a2fbc48fc20a2cd83418227b21.pdf
dx.doi.org/10.22052/ijmc.2012.5274
On Counting Polynomials of Some Nanostructures
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
M.
SONGHORI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
Supplement 1
no.
2012
51
58
http://ijmc.kashanu.ac.ir/article_5275_598bbbb545b1a47f060eba52713bf436.pdf
dx.doi.org/10.22052/ijmc.2012.5275
Computing Chemical Properties of Molecules by Graphs and Rank Polynomials
M.
MOGHARRAB
Persian Gulf University,
I.R. Iran
author
G.
FATH-TABAR
University of
Kashan, I. R. Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
Supplement 1
no.
2012
59
65
http://ijmc.kashanu.ac.ir/article_5276_79a271992b7bcfde9d597fe6eba83405.pdf
dx.doi.org/10.22052/ijmc.2012.5276
A Note on Atom Bond Connectivity Index
S.
HEIDARI RAD
Shahid Rajaee Teacher Training
University, I. R. Iran
author
A.
KHAKI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
text
article
2012
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
3
v.
Supplement 1
no.
2012
67
75
http://ijmc.kashanu.ac.ir/article_5277_d209553fa79f35c61cae445c78d6baa4.pdf
dx.doi.org/10.22052/ijmc.2012.5277