Detour Global Domination for k-Regular Graphs with Girth 3 Where k is Even

Abstract

In this paper, we introduced the new concept detour global domination number for -regular graph with girth 3, where  is even. First we recollect the concept of -regular graphs and we produce some results based on the detour global domination number for -regular graph with girth 3, where  is even. 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 .