eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-12-01
3
Supplement 1
1
5
10.22052/ijmc.2012.5269
5269
Note on Properties of First Zagreb Index of Graphs
M. TAVAKOLI
1
F. RAHBARNIA
2
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
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
Topological indices
The first and second Zagreb indices
Tree
Graph operation
Strongly distance-balanced graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-12-01
3
Supplement 1
7
18
10.22052/ijmc.2012.5270
5270
Eccentric Connectivity Index of Some Dendrimer Graphs
M. GHORBANI
1
KH. MALEKJANI
2
A. KHAKI
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;
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
Eccentricity
Topological index
Dendrimer graphs
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-12-01
3
Supplement 1
19
28
10.22052/ijmc.2012.5271
5271
Computing GA4 Index of Some Graph Operations
M. SAHELI
1
M. JALALI RAD
2
University of Kashan, I. R. Iran
University of Kashan, Kashan, I. R. Iran
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
Topological index
GA Index
GA_{4} index
Graph operations
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-12-01
3
Supplement 1
29
36
10.22052/ijmc.2012.5272
5272
On Symmetry of Some Nano Structures
M. GHORBANI
1
A. ZAEEMBASHI
2
M. SHAHREZAEI
3
A. TABATABAEI ADNANI
4
Shahid Rajaee Teacher Training University, I. R. Iran
Shahid Rajaee Teacher Training University, I. R. Iran
Imam Hossein University, I.R. Iran
Islamic Azad University, I. R. Iran
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
Weighted graph
Euclidean graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-12-01
3
Supplement 1
37
43
10.22052/ijmc.2012.5273
5273
Applications of Graph Operations
M. TAVAKOLI
1
F. RAHBARNIA
2
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
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
Topological index
Graph operation
Hierarchical product
Chemical graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-12-01
3
Supplement 1
45
50
10.22052/ijmc.2012.5274
5274
Geometric-Arithmetic Index of Hamiltonian Fullerenes
H. MOSTAFAEI
1
A. ZAEEMBASHI
2
M. OSTAD RAHIMI
3
Islamic Azad University, Tehran, Iran
Shahid Rajaee Teacher Training University, Tehran, I. R. Iran
Tehran North Branch, Islamic Azad University, Iran
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
Fullerene graphs
Hamiltonian graphs
Geometric –arithmetic index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-12-01
3
Supplement 1
51
58
10.22052/ijmc.2012.5275
5275
On Counting Polynomials of Some Nanostructures
M. GHORBANI
1
M. SONGHORI
2
Shahid Rajaee Teacher Training University, I. R. Iran
Shahid Rajaee Teacher Training University, I. R. Iran
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
Omega polynomial
PI polynomial
Nanostar dendrimers
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-12-01
3
Supplement 1
59
65
10.22052/ijmc.2012.5276
5276
Computing Chemical Properties of Molecules by Graphs and Rank Polynomials
M. MOGHARRAB
1
G. FATH-TABAR
2
Persian Gulf University, I.R. Iran
University of Kashan, I. R. Iran
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
Dendrimers
Tutte polynomial
PI-polynomial
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2012-12-01
3
Supplement 1
67
75
10.22052/ijmc.2012.5277
5277
A Note on Atom Bond Connectivity Index
S. HEIDARI RAD
1
A. KHAKI
2
Shahid Rajaee Teacher Training University, I. R. Iran
Shahid Rajaee Teacher Training University, I. R. Iran
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
Topological index
ABC Index
Nanotube
Nanotori