Semi-strong split domination in graphs

Document Type: Research Paper

Authors

1 Department of Studies in Mathematics, University of Mysore, Mysore-570006 Karnataka, India

2 National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, Krishnankoil-626126, India

Abstract

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

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