Detour Global Domination for Splitting Graph of Path, Cycle, Wheel and Helm graph

Abstract

In this paper, we introduced the new concept detour global domination number for splitting graph of Path, Cycle, Wheel and Helm graph. First we recollect the concept of splitting graph of a graph and we produce some results based on the detour global domination number of splitting graph of path graph, cycle graph, wheel graph and helm graph. A set  is called a detour global dominating set of  if  is both detour and global dominating set of . The detour global domination number is the minimum cardinality of a detour global dominating set in .