Power Domination Parameters in Honeycomb-Like Networks

A set S of vertices in a graph G is called a dominating set of G if every vertex in V (G)�S is adjacent to some vertex in S. A set S is said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. The power domination number of G is the minimum cardinality of a power dominating set of G. In this paper, we obtain the power domination number for triangular graphs, pyrene networks, circum-pyrene networks, circum-trizene networks, generalized honeycomb torus and honeycomb rectangular torus. © Springer Nature Switzerland AG 2019.