Abstract
A subset \( H \subseteq V (G) \) of a graph \(G\) is a hop dominating set (HDS) if for every \({v\in (V\setminus H)}\) there is at least one vertex \(u\in H\) such that \(d(u,v)=2\). The minimum cardinality of a hop dominating set of \(G\) is called the hop domination number of \(G\) and is denoted by \(\gamma_{h}(G)\). In this paper, we compute the hop domination number for triangular and quadrilateral snakes. Also, we analyse the hop domination number of graph families such as generalized thorn path, generalized ciliates graphs, glued path graphs and generalized theta graphs.
Highlights
Domination in graphs is fascinating topic in the field of graph theory
Packiavathi et al [6] obtained the hop domination number of a caterpillar graph Pn(l1, l2, . . . , ln) and the domination number for some special families of snake graphs which occur as hop graph of Pn(1, 1, . . . , 1) and Pn(2, 2, . . . , 2)
We study our parameter namely, hop domination number for thorn rod given in [4], as well as for other generalized graph structures
Summary
Domination in graphs is fascinating topic in the field of graph theory. It is one of the most effective mathematical models for a variety of real world problems. Ayyasamy et al [1] defined a new distance-based domination parameter called the hop domination number of a graph G. Natarajan et al [13] found characterization results for hop domination number equals other domination parameters like total domination number, connected domination number for several families of graphs. Ln) (a caterpillar is a graph obtained from the path by attaching leaves li to ith vertex of the path Pn) and the domination number for some special families of snake graphs which occur as hop graph of Pn(1, 1, . We refine their result on caterpillar graph and present an elegant result
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