@Article{Ediz2012,
author="Ediz, Suleyman",
title="The augmented eccentric connectivity index of nanotubes and nanotori",
journal="Journal of Mathematical Nanoscience",
year="2012",
volume="2",
number="1-2",
pages="1-8",
abstract="Let G be a connected graph, the augmented eccentric connectivity index is a topological index was defined as $\zeta(G)=\sum_{i=1}^nM_i/E_i$, where Mi is the product of degrees of all vertices vj, adjacent to vertex vi, Ei is the largest distance between vi and any other vertex vk of G or the eccentricity of i v and n is the number of vertices in graph G. In this paper exact formulas for the augmented eccentric connectivity index of TUC4C8(S) nanotube and TC4C8(R) nanotorus are given.",
issn="2538-2314",
doi="10.22061/jmns.2012.465",
url="http://jmathnano.sru.ac.ir/article_465.html"
}
@Article{Sharafdini2012,
author="Sharafdini, Reza",
title="Hosoya index of bridge and splice graphs",
journal="Journal of Mathematical Nanoscience",
year="2012",
volume="2",
number="1-2",
pages="9-13",
abstract="The Hosoya index of a graph is defined as the total number of the matchings (including the empty edge set) of the graph. In this paper, explicit formulas are given for the Hosoya index of bridge and splice graphs.",
issn="2538-2314",
doi="10.22061/jmns.2012.469",
url="http://jmathnano.sru.ac.ir/article_469.html"
}
@Article{Farahani2012,
author="Farahani, Mohammad",
title="A new version of Zagreb index of circumcoronene series of benzenoid",
journal="Journal of Mathematical Nanoscience",
year="2012",
volume="2",
number="1-2",
pages="15-20",
abstract="Among topological indices, Zagreb indices are very important, very old and they have many useful properties in chemistry and specially in mathematics chemistry. First and second Zagreb indices have been introduced by Gutman and Trinajstić as $M_1(G)=\sum_{uv\in E}d_u+d_v$ and $M_1(G)=\sum_{uv\in E}d_ud_v$, where du denotes the degree of vertex u in G. Recently, we know new versions of Zagreb indices as $M_1^{*}(G)=\sum_{uv\in E}ecc(u)+ecc(v)$, $M_1^{**}(G)=\sum_{u\in V}ecc(u)^2$ and $M_2^{*}(G)=\sum_{uv\in E}ecc(u)ecc(v)$, where ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we focus one of these new topological indices that we call fifth Zagreb index $M_2^*(G)=M_5(G)$ and we compute this index for a famous molecular graph Circumcoronene series of benzenoid Hk, k≥ 1.",
issn="2538-2314",
doi="10.22061/jmns.2012.466",
url="http://jmathnano.sru.ac.ir/article_466.html"
}
@Article{Songhori2012,
author="Songhori, Mahin",
title="Eccentric connectivity index of fullerene graphs",
journal="Journal of Mathematical Nanoscience",
year="2012",
volume="2",
number="1-2",
pages="21-27",
abstract="The eccentric connectivity index of the molecular graph is defined as $\zeta^c(G)=\sum_{uv\in E}degG(u)ε(u)$ , where degG(x) denotes the degree of the vertex x in G and ε(u)=max{d(x,u) |x ε V(G)}. In this paper this polynomial is computed for an infinite class of fullerenes.",
issn="2538-2314",
doi="10.22061/jmns.2012.467",
url="http://jmathnano.sru.ac.ir/article_467.html"
}
@Article{Nik-Andish2012,
author="Nik-Andish, Somayyeh",
title="Remarks on atom bond connectivity index",
journal="Journal of Mathematical Nanoscience",
year="2012",
volume="2",
number="1-2",
pages="29-36",
abstract="A topological index is a function Top from Σ into real numbers with this property that Top(G) = Top(H), if G and H are isomorphic. Nowadays, many of topological indices were defined for different purposes. In the present paper we present some properties of atom bond connectivity index.",
issn="2538-2314",
doi="10.22061/jmns.2012.468",
url="http://jmathnano.sru.ac.ir/article_468.html"
}
@Article{Songhori2012,
author="Songhori, Mahin",
title="A note on eccentric distance sum",
journal="Journal of Mathematical Nanoscience",
year="2012",
volume="2",
number="1-2",
pages="37-41",
abstract="The eccentric distance sum is a graph invariant defined as $\sum_{uv\in E} εG(v)DG(v)$, where εG(v) is the eccentricity of a vertex v in G and DG(v ) is the sum of distances of all vertices in G from v. In this paper, we compute the eccentric distance sum of Volkmann tree and then we obtain some results for vertex−transitive graphs",
issn="2538-2314",
doi="10.22061/jmns.2012.470",
url="http://jmathnano.sru.ac.ir/article_470.html"
}