Tadpole domination number of graphs

Abstract

The graph obtained by joining cycle [Formula: see text] to a path [Formula: see text] with a bridge is called Tadpole graph denoted by [Formula: see text]. A subset [Formula: see text] of [Formula: see text] is said to be a tadpole dominating set of [Formula: see text] if [Formula: see text] is a dominating set and the set of vertices of [Formula: see text] spans a tadpole graph [Formula: see text] where [Formula: see text], [Formula: see text]. In this paper, we find the tadpole domination number of cartesian product of certain graphs, namely, paths, cycles and complete graphs. Also the tadpole domination number for the Mycielskian of cycles and paths is obtained.