Connected Co-Independent Hop Domination in the Edge Corona and Complementary Prism of Graphs

Abstract

Let $G$ be a connected graph. A subset $S$ of $V(G)$ is a connected co-independent hop dominating set in $G$ if the subgraph induced by $S$ is connected and $V(G)\mathrm{\setminus }S$ is an independent set where for each $v\in V(G)\mathrm{\setminus }S$, there exists a vertex $u\in S$ such that $d_G(u,v)=2$. The smallest cardinality of such an $S$ is called the connected co-independent hop domination number of $G$. This paper presents the characterizations of the connected co-independent hop dominating sets in the edge corona and complementary prism of graphs and determines the exact values of their corresponding connected co-independent hop domination number.