INVERSE AND CONNECTED DOMINATION IN HYPERTREE NETWORKS

A dominating set of a graph \( G = (V, E) \) is a subset $D$ of vertices such that every vertex in \( V \setminus D \) is adjacent to at least one vertex in \( D \), and the minimum size of such a set is called the domination number denoted by \( \gamma(G) \). If \( D \) is a minimum dominating set of \( G \) and there exists a dominating set \( D' \) within \( V \setminus D \), 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 \( \gamma'(G) \).A dominating set \( D \) is called a connected dominating set if the induced subgraph \( \langle D \rangle \) is connected in \( G \). The minimum cardinality of a connected dominating set is called the connected domination number, denoted by \( \gamma_{c}(G) \). In this paper, we have computed the inverse and connected domination numbers for Hypertree Networks.