Strong Co-Secure Domination in Graphs

Abstract

Let be a graph. A subset  of the vertex set  of a graph  is a strong co-secure dominating set if every vertex  there exists  such that  then  and. The strong co-secure domination number is the minimum cardinality of a strong co-secure dominating set of  and it is denoted by. The strong co-secure dominating set of  is found for path, cycle, helm graph, closed helm graph, Petersen graph, gear graph, Tadpole graph, and Butterfly graph.