@Article{Reti2011,
author="Reti, Tamas
and Gutman, Ivan
and Vukicevic, Damir",
title="On Zagreb indices of pseudo-regular graphs",
journal="Journal of Mathematical Nanoscience",
year="2011",
volume="1",
number="1-2",
pages="1-12",
abstract="Properties of the Zagreb indices of pseudo-regular graphs are established, with emphasis on the Zagreb indices inequality. The relevance of the results obtained for the theory of nanomolecules is pointed out.",
issn="2538-2314",
doi="10.22061/jmns.2011.458",
url="http://jmathnano.sru.ac.ir/article_458.html"
}
@Article{Dong2011,
author="Dong, Hui
and Zhou, Bo",
title="Szeged index of bipartite unicyclic graphs",
journal="Journal of Mathematical Nanoscience",
year="2011",
volume="1",
number="1-2",
pages="13-24",
abstract="The Szeged index of a connected graph G is defined as the sum of products n1(e|G)n2(e|G) over all edges e = uv of G where n1(e|G) and n2(e|G) are respectively the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u In this paper, we determine the n-vertex bipartite unicyclic graphs with the first, the second, the third and the fourth smallest Szeged indices.",
issn="2538-2314",
doi="10.22061/jmns.2011.459",
url="http://jmathnano.sru.ac.ir/article_459.html"
}
@Article{Doslic2011,
author="Doslic, Tomislav
and Salehi, Mahboobeh",
title="Augmented eccentric connectivity index of single defect nanocones",
journal="Journal of Mathematical Nanoscience",
year="2011",
volume="1",
number="1-2",
pages="25-31",
abstract="We present explicit formulas for the values of augmented eccentric connectivity indices of single-defect nanocones. Our main result is that the augmented eccentricity index of an n-layer nanocone with a single k-gonal defect at its apex behaves asymptotically 27k(1- ln 2)n for k ≥ 5 .",
issn="2538-2314",
doi="10.22061/jmns.2011.460",
url="http://jmathnano.sru.ac.ir/article_460.html"
}
@Article{Graovac2011,
author="Graovac, Ante
and Ghorbani, Modjtaba
and Hosseinzadeh, Mohammad Ali",
title="Computing fifth geometric-arithmetic index for nanostar dendrimers",
journal="Journal of Mathematical Nanoscience",
year="2011",
volume="1",
number="1-2",
pages="33-42",
abstract="The geometric-arithmetic index is a topological index was defined as GA(G)=∑uv2(dudv)1/2/(du+dv), in which degree of vertex u denoted by dG(u ). Now we define a new version of GA index as GA5(G)=∑uv2(δuδv)1/2/(δu+δv) , where δu=∑uvdv. The goal of this paper is to further the study of the GA5 index.",
issn="2538-2314",
doi="10.22061/jmns.2011.461",
url="http://jmathnano.sru.ac.ir/article_461.html"
}
@Article{Ghorbani2011,
author="Ghorbani, Modjtaba",
title="Connective eccentric index of fullerenes",
journal="Journal of Mathematical Nanoscience",
year="2011",
volume="1",
number="1-2",
pages="43-50",
abstract="Fullerenes are carbon-cage molecules in which a number of carbon atoms are bonded in a nearly spherical configuration. The connective eccentric index of graph G is defined as C (G)= Σa V(G)deg(a)ε(a) -1, where ε(a) is defined as the length of a maximal path connecting a to another vertex of G. In the present paper we compute some bounds of the connective eccentric index and then we calculate this topological index for two infinite classes of fullerenes.",
issn="2538-2314",
doi="10.22061/jmns.2011.462",
url="http://jmathnano.sru.ac.ir/article_462.html"
}
@Article{Alikhani2011,
author="Alikhani, Saeid",
title="Hosoya index and Fibonacci numbers",
journal="Journal of Mathematical Nanoscience",
year="2011",
volume="1",
number="1-2",
pages="51-57",
abstract="Let G =(V ,E) be a simple graph. The Hosoya index Z(G) of G is defined as the total number of edge independent sets of G . Fibonacci numbers are terms of the sequence defined in a quite simple recursive fashion. In this paper, we investigate the relationships between Hosoya index and Fibonacci numbers. Also we consider Fibonacci cubes and study some of its parameters which is related to Fibonacci numbers.",
issn="2538-2314",
doi="10.22061/jmns.2011.463",
url="http://jmathnano.sru.ac.ir/article_463.html"
}
@Article{Salahshour2011,
author="Salahshour, Mohammad Ali",
title="The PI and vertex PI polynomial of dendimers",
journal="Journal of Mathematical Nanoscience",
year="2011",
volume="1",
number="1-2",
pages="59-65",
abstract="Let G be a simple connected graph. The vertex PI polynomial of G is defined as PIv(G ,x )=Σe=uv Xnu(e)+nv(e) here nu(e) is the number of vertices closer to u than v and nv(e) is the number of vertices closer to v than u. The PI polynomial of G is defined as PI(G ,x )=Σe=uv Xmu(e)+mv(e) , where mu(e) is the number of edges closer to u than v and mv(e) is the number of edges closer to v than u. In this paper, the PI and vertex PI polynomials of two types of dendrimers are computed.",
issn="2538-2314",
doi="10.22061/jmns.2011.464",
url="http://jmathnano.sru.ac.ir/article_464.html"
}