Extension of the Wiener index and Wiener polynomial
نویسندگان
چکیده
منابع مشابه
The Hyper-Wiener Polynomial of Graphs
The distance $d(u,v)$ between two vertices $u$ and $v$ of a graph $G$ is equal to the length of a shortest path that connects $u$ and $v$. Define $WW(G,x) = 1/2sum_{{ a,b } subseteq V(G)}x^{d(a,b) + d^2(a,b)}$, where $d(G)$ is the greatest distance between any two vertices. In this paper the hyper-Wiener polynomials of the Cartesian product, composition, join and disjunction of graphs are compu...
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The Hosoya polynomial of a graph, H(G, z), has the property that its first derivative, evaluated at z = 1, equals the Wiener index, i.e., W(G) = H’(G, 1). In this paper, an equation is presented that gives the hyper-Wiener index, WW(G), in terms of the first and second derivatives of H(G,z). Also defined here is a hyper-Hosoya polynomial, HH(G,r), which has the property WW(G) = HH’(G, l), analo...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2008
ISSN: 0893-9659
DOI: 10.1016/j.aml.2007.10.001