Abstract
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 K2 ◊ H, where H is a path graph Pn, cyclic graph Cn, or star graph Sn, with n vertices (These are called: ladder graph, prism graph, and book graph).
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