Abstract
A subset M of the edge set E (G) of a graph G is a matching if no two edges of M are adjacent in G. In this paper we study the number of matchings in graphs, that is the Hosoya index. We study the problem of maximizing and minimizing the Hosoya index in a graph. For specific graphs this topological index is maximized by the Fibonacci number or the Lucas number. Next we give the generalizations of the Fibonacci number and the Lucas number which give the number of matchings in special multigraphs.
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