Semi-strong split domination in graphs

Abstract

Given a graph $G=(V,E)$‎, ‎a dominating set $Dsubseteq V$ is called a <em>semi-strong split dominating set</em> of $G$ if $|Vsetminus D|geq1$ and the maximum degree of the induced subgraph $langle Vsetminus D rangle$ is $1$‎. ‎The cardinality of a minimum semi-strong split dominating set (SSSDS) of $G$ is the <em>semi-strong split domination number</em> of $G$‎, ‎denoted $gamma_{sss}(G)$‎. ‎In this paper‎, ‎we introduce the concept and prove several results regarding it‎.