The n-Hosoya Polynomials of Some Classes of Thorn Graphs
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چکیده
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The Merrifield-Simmons indices and Hosoya indices of some classes of cartesian graph product
The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...
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let $g=(v,e)$ be a simple graph of order $n$ and size $m$. an $r$-matching of $g$ is a set of $r$ edges of $g$ which no two of them have common vertex. the hosoya index $z(g)$ of a graph $g$ is defined as the total number of its matchings. an independent set of $g$ is a set of vertices where no two vertices are adjacent. the merrifield-simmons index of $g$ is defined as the tota...
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The Hosoya polynomial of a graph encompasses many of its metric properties, for instance the Wiener index (alias average distance) and the hyperWiener index. An expression is obtained that reduces the computation of the Hosoya polynomials of a graph with cut vertices to the Hosoya polynomial of the so-called primary subgraphs. The main theorem is applied to specific constructions including bouq...
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The Hosoya index of a graph is defined as the total number of its matchings. In this paper, we obtain that the largest Hosoya index of (n, n+1)-graphs is f (n+1)+f (n−1)+2f (n−3), where f (n) is the nth Fibonacci number, and we characterize the extremal graphs. © 2008 Elsevier Ltd. All rights reserved.
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ژورنال
عنوان ژورنال: AL-Rafidain Journal of Computer Sciences and Mathematics
سال: 2010
ISSN: 2311-7990
DOI: 10.33899/csmj.2010.163848