Degree Splitting Graphs of Certain Classes of Graphs with Small Power Domination Number

Abstract

A set  of vertices is defined to be a power dominating set of a graph  if every vertex and every edge in the system is monitored by the set  (according to a set of rules for power system monitoring). The minimum number of elements of a power dominating set of a graph  is the power domination number  When operations on graphs are carried out, the original graphs under consideration give rise to new types of graphs. The degree splitting is one such operation, having some applications as well. In this paper, we compute the power domination number  for degree splitting graphs of certain classes of graphs.