A variation of distance domination in composite networks

Abstract

Let V be the set of vertex of a graph G. The set S is a dominating set, being a subset of the set V, if every vertex in the set V is in the set S, or if it is neighbor of a vertex in the set S. The number of elements of the set S with the least number of elements is the dominating number of graph G. In this study, we have worked on a type of dominating called porous exponential domination. In this new parameter, while the distance between vertex s and vertex v grows this weight value reduces exponentially. If all vertices in S dominate all vertices of G a with a total weight of at least 1, the set S is named as a porous exponential dominating set of graph G. The cardinality of the set with the least number of elements of the obtained porous exponential domination sets is defined as the porous exponential domination number of graph G. In this paper we compute the porous exponential domination number of the R - graphs under corona and join product.