Valency based domination number for Mycielskian of some graphs

Let G = (V, E) be a connected graph and γvb(G) denotes the valency based domination number of G or simply vb-domination number of G. In this paper, analogous to isolated vertex in domination, defined valency based isolated vertex (or simply, vb-isolated vertex ) in vb-domination and proved that vb-isolated vertices belong to any vb-dominating set. Also studied its properties in the graph G as well as in its Mycielskian, µ(G). Established an inequality connecting vb-domination number of Mycielskian of G and domination number of G. Obatined an upper bound for vb-domination number of Mycielskian of regulargraphs. Also calculated vb-domination number of Mycielskian of some graph classes.