Connected Co-Independent Hop Domination in the Edge Corona and Complementary Prism of Graphs
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i4.5342Keywords:
hop dominating set, Strictly co-independent set,, edge coronaAbstract
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 $V(G) \backslash S$ is an independent set where for each $v \in V(G) \backslash S$, 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.
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Copyright (c) 2024 Sandra Nanding, Helen M. Rara, Imelda S. Aniversaro
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