Another Look at Geodetic Hop Domination in a Graph.

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 set and a hop dominating set. The geodetic hop domination number of G is the minimum cardinality among all geodetic hop dominating sets in G. In this paper, we characterize the geodetic hop dominating sets in the join of two graphs. These characterizations which use the concept of pointwise non-dominating 2-path closure absorbing set are, in turn, used to determine the geodetic hop domination number of the join of graphs. Moreover, a realization result involving the hop domination number and geodetic hop domination number is also obtained. [ABSTRACT FROM AUTHOR]