Revisiting Domination, Hop Domination, and Global Hop Domination in Graphs

A set S subset of V(G) is a hop dominating set of G if for each v is an element of V (G) \ S, there exists w is an element of S such that d(G)(v, w) = 2. It is a global hop dominating set of G if it is a hop dominating set of both G and the complement (G) over bar of G. The minimum cardinality of a hop dominating (global hop dominating) set of G, denoted by gamma(h)(G) (resp. gamma(gh)(G)), is called the hop domination (resp. global hop domination) number of G. In this paper, we give some realization results involving domination, hop domination, and global hop domination parameters. Also, we give a rectification of a result found in a recent paper of the authors and use this to prove some results in this paper.