Disjunctive Total Domination of Some Shadow Distance Graphs

Abstract

Let $ G $ be a graph having vertex set $ V(G) $. For $ S\subseteq V(G) $, if each vertex is adjacent to a vertex in $ S $ or has at least two vertices in $ S $ at distance two from it, then the set $ S $ is a disjunctive total dominating set of $ G $. The disjunctive total domination number is the minimum cardinality of such a set. In this work, we discuss the disjunctive total domination of shadow distance graphs of some graphs such as cycle, path, star, complete bipartite and wheel graphs.