منابع مشابه
The Hosoya polynomial decomposition for hexagonal chains
For a graph G we denote by dG(u, v) the distance between vertices u and v in G, by dG(u) the degree of vertex u. The Hosoya polynomial of G is H(G) = ∑ {u,v}⊆V (G) x dG (u,v). For any positive numbers m and n, the partial Hosoya polynomials of G are Hm(G) = ∑ {u, v} ⊆ V (G) dG (u) = dG (v) = m xdG (u,v), Hmn(G) = ∑ {u, v} ⊆ V (G) dG (u) = m, dG (v) = n xdG (u,v). It has been shown that H(G1) − ...
متن کاملSome New Results On the Hosoya Polynomial of Graph Operations
The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...
متن کاملHosoya polynomials of random benzenoid chains
Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...
متن کاملextensions of some polynomial inequalities to the polar derivative
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15 صفحه اولOn the Roots of Hosoya Polynomial of a Graph
Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...
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ژورنال
عنوان ژورنال: Cogent Mathematics
سال: 2017
ISSN: 2331-1835
DOI: 10.1080/23311835.2017.1305638