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 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).