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