Restrained captive domination number

Abstract

The restrained captive domination number (RCDN), denoted by γRca(G),{\gamma }_{{\rm{Rca}}}(G), is a new definition of domination number in graphs introduced in this article. If DD is a captive dominating set and G[V−D]G{[}V-D] has no isolated vertex, then DD is a restrained captive dominating set (RCDS) of graph GG. 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.

Keywords

• restrained captive domination number
• restrained captive dominating set
• inverse
• complement