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 𝑆is called a detour global dominating setof 𝐺if 𝑆is both detour and global dominating set of 𝐺. The detour global domination numberis the minimum cardinality of a detour global dominating set in 𝐺.