Merrifield-Simmons index of Cartesian product of two graphs

Abstract

Merrifield-Simmons index of a graph G shorted word M-S index, noted by σ(G), which is defined as the number of the independent sets of the graph G. In this paper, a special graph is defined and considered the Merrifield-Simmons index. The main concer in this work is devoted to calculating the number of independent sets with respect to the Cartesian product of Sm and Pn , where Sm is a star of order m and Pn is a path of order n, respectively.