Restrained captive domination number

Abstract

Abstract The restrained captive domination number (RCDN), denoted by γ Rca ( G ) , {\gamma }_{{\rm{Rca}}}(G), is a new definition of domination number in graphs introduced in this article. If D D is a captive dominating set and G [ V − D ] G{[}V-D] has no isolated vertex, then D D is a restrained captive dominating set (RCDS) of graph G G . Furthermore, some properties, theorems, and propositions are determined. The inverse RCDN is introduced too. The RCDN in complement graphs is discussed. Finally, the RCDS of some graphs is determined. We have explained that if the graph has pendent vertex, then it has no RCDN.