Connected cototal domination number of a graph

Abstract

A dominating set $D subseteq V$ of a graph $G = (V,E)$ is said to be a connected cototal dominating set if $langle D rangle$ is connected and $langle V-D rangle neq phi$, contains no isolated vertices. A connected cototal dominating set is said to be minimal if no proper subset of $D$ is connected cototal dominating set. The connected cototal domination number $gamma_{ccl}(G)$ of $G$ is the minimum cardinality of a minimal connected cototal dominating set of $G$. In this paper, we begin an investigation of connected cototal domination number and obtain some interesting results.

Keywords

• domination number
• connected domination number
• cototal domination number and connected cototal domination number