Minimum Dominating Set for the Prism Graph Family

Abstract

The dominating set of the graph G is a subset D of vertex set V, such that every vertex not in V-D is adjacent to at least one vertex in the vertex subset D. A dominating set D is a minimal dominating set if no proper subset of D is a dominating set. The number of elements in such set is called as domination number of graph and is denoted by $\gamma(G)$. In this work the domination numbers are obtained for family of prism graphs such as prism CL_n, antiprism Q_n and crossed prism R_n by identifying one of their minimum dominating set.