Power Domination in Certain Nanotori

J. Anitha1
1Department of Mathematics, Easwari Engineering College, Chennai, India-600 089.

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, \(C_5C_6C_7[m,n]\) nanotori and \(C_4C_6C_8[m,n]\) nanotori.

Keywords: Power domination; H-Naphtelanic/m, n] nanotori; C5C6C7m, n); C4C6C8[m, n] nanotori.