Semi-strong split domination in graphs

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