Porous exponential domination number of some graphs

Abstract

Let G be a graph and S subset of V(G). If n-ary sumation u is an element of S12d(u,v)-1 >= 1 for all v is an element of V(G), then S is a porous exponential dominating set for G, where d(u, v) is the distance between vertices u and v. The smallest cardinality of a porous exponential dominating set is the porous exponential domination number of G and is denoted by gamma e*(G). In this article, we examine porous exponential domination number of some shadow graphs and trees such as comet, double comet, double star, binomial tree, and generalized caterpillar graphs.