Inverse and connected domination in Hypertree Networks

Abstract

A dominating set of a graph G = (V, E) is a subset D of vertices such that every vertex in V \ D is adjacent to at least one vertex in D, and the minimum size of such a set is called the domination number denoted by γ(G). If D is a minimum dominating set of G and there exists a dominating set D′ within V \ D, then D′ is called an inverse dominating set with respect to D. The minimum cardinality of such a set is known as the inverse domination number, denoted by γ′ (G). A dominating set D is called a connected dominating set if the induced subgraph ⟨D⟩ is connected in G. The minimum cardinality of a connected dominating set is called the connected domination number, denoted by γc(G). In this paper, we have computed the inverse and connected domination numbers for Hypertree Networks.