Power Domination in Certain Nanotori

Abstract

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 solve the power domination number for certain nanotori such as H-Naphtelanic, $C_5{C}_6{C}_7[m,n]$ nanotori and $C_4{C}_6{C}_8[m,n]$ nanotori.