Abstract
Merrifield-Simmons index of a graph G shorted word M-S index, which is denoted as the number of the independent sets of the graph G. For a graph G, an independent set is a subset I of which vertex set V(G) that there is not edge of G between every two vertices of I. In this work, several special graphs are defined and the M-S indices of these graphs are obtained. Based on that, the M-S indices of GH, G×H, G•H and G H are given, where G is a cycle of order 3 or a star of order t, and H is a complete graph Kn, of order n.
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