An Optimal Algorithm to Find Minimum K-hop Dominating Set

Domination in graphs has been an extensively researched branch of graph theory. Among the variations of dominations, k-hop domination has been briey discussed in the past and it has important applications in communication networks.In this book, we consider the problem of nding a minimum k-hop dominating set of interval graphs. For this purpose, we rst construct the BFS-tree T with root as 1. After then we identify the main path of the BFS-tree T. Next we nd the rst member of k-hop dominating set of interval graph, by using some results. Then we nd the next member of k-hop dominating set by a procedure FindNext. Here,we proposed an O(n) time algorithm to nd a minimum k-hop dominating set of undirected and connected interval graphs with n vertices.