Another Look at Geodetic Hop Domination in a Graph
Keywords:hop domination, Geodetic hop domination, join
Let $G$ be an undirected graph with vertex and edge sets $V(G)$ and $E(G)$, respectively. A subset $S$ of vertices of $G$ is a geodetic hop dominating set if it is both a geodetic and a hop dominating set. The geodetic hop domination number of $G$ is the minimum cardinality among all geodetic hop dominating sets in $G$. Geodetic hop dominating sets in a graph resulting from the join of two graphs have been characterized. These characterizations have been used to determine the geodetic hop domination number of the graphs considered. A realization result involving the hop domination number and geodetic hop domination number is also obtained.
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