ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES

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.

Keywords

• hop domination number, snake graphs, theta graphs, generalized thorn path