2020-08-07T20:46:04Z
https://ijmc.kashanu.ac.ir/?_action=export&rf=summon&issue=880
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
Supplement 1
Note on Properties of First Zagreb Index of Graphs
M.
TAVAKOLI
F.
RAHBARNIA
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
2012
12
01
1
5
https://ijmc.kashanu.ac.ir/article_5269_88e60cb49fa19ed72edeae0db9befde3.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
Supplement 1
Eccentric Connectivity Index of Some Dendrimer Graphs
M.
GHORBANI
KH.
MALEKJANI
A.
KHAKI
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
2012
12
01
7
18
https://ijmc.kashanu.ac.ir/article_5270_22121ef8fc11a8b1d9590fd604033097.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
Supplement 1
Computing GA4 Index of Some Graph Operations
M.
SAHELI
M.
JALALI RAD
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
2012
12
01
19
28
https://ijmc.kashanu.ac.ir/article_5271_e45e1b12bd7d45ac826b874c26ef0661.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
Supplement 1
On Symmetry of Some Nano Structures
M.
GHORBANI
A.
ZAEEMBASHI
M.
SHAHREZAEI
A.
TABATABAEI ADNANI
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
2012
12
01
29
36
https://ijmc.kashanu.ac.ir/article_5272_4354587496110c6a075b0d1990485b94.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
Supplement 1
Applications of Graph Operations
M.
TAVAKOLI
F.
RAHBARNIA
In this paper, some applications of our earlier results in working with chemical graphs are presented.
topological index
Graph operation
Hierarchical product
Chemical graph
2012
12
01
37
43
https://ijmc.kashanu.ac.ir/article_5273_84937ba7dd780549b008d14ef626f331.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
Supplement 1
Geometric-Arithmetic Index of Hamiltonian Fullerenes
H.
MOSTAFAEI
A.
ZAEEMBASHI
M.
OSTAD RAHIMI
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
2012
12
01
45
50
https://ijmc.kashanu.ac.ir/article_5274_132874a2fbc48fc20a2cd83418227b21.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
Supplement 1
On Counting Polynomials of Some Nanostructures
M.
GHORBANI
M.
SONGHORI
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
2012
12
01
51
58
https://ijmc.kashanu.ac.ir/article_5275_598bbbb545b1a47f060eba52713bf436.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
Supplement 1
Computing Chemical Properties of Molecules by Graphs and Rank Polynomials
M.
MOGHARRAB
G.
FATH-TABAR
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
2012
12
01
59
65
https://ijmc.kashanu.ac.ir/article_5276_79a271992b7bcfde9d597fe6eba83405.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2012
3
Supplement 1
A Note on Atom Bond Connectivity Index
S.
HEIDARI RAD
A.
KHAKI
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
2012
12
01
67
75
https://ijmc.kashanu.ac.ir/article_5277_d209553fa79f35c61cae445c78d6baa4.pdf