Set Domination Number of Jump Graph

Abstract

Let $G = (V,E)$ be a connected graph. A Set $D\subseteq V(J(G))$ is a set dominating set (sd-set) of jump graph if for every set $T \subset V(J(G))-D$, there exists a non empty set $S \subset D$ such that the subgraph $\langle S \cup T\rangle$ induced by $S \cup T$ is connected. The set domination number $\gamma_s(J(G))$ of $J(G)$ is the minimum cardinality of a sd-set of $J(G)$ .We also study the graph theoretic properties of $\gamma_s(J(G))$ and its exact values of some standard graphs. The relation between $\gamma_s(J(G))$ with other parameters is also investigated.