Disjunctive Total Domination In Harary Graphs

Abstract

Let $ G $ be a graph. A set $ S $ of vertices in $ G $ is a disjunctive total dominating set of $ G $ if every vertex is adjacent to a vertex of $ S $ or has at least two vertices in $ S $ at distance two from it. The disjunctive total domination number, $ \gamma _t^d(G) $, is the minimum cardinality of such a set. In this paper, we determine disjunctive total domination number of Harary graph $ H_{k,n} $ for all $ k $ and $ n $.