On ve-quasi and secured ve-quasi independent sets of a graph

Abstract

In this paper, we have defined the concepts of ve-quasi independent set and secured ve-quasi independent set. In order to define these concepts we have used the concept of a vertex which m-dominates an edge. We prove a characterization of a maximal ve-quasi independent set. We also prove that the complement of a ve-quasi independent set is a ve-dominating set. We prove a necessary and sufficient condition under which a ve-quasi independent set is a secured ve-quasi independent set. Also we prove a necessary and sufficient condition under which the ve-quasi independence number and secured ve-quasi independence number decrease when a vertex is removed from the graph. Some examples have also been given. Keywords ve-quasi independent set, secured ve-quasi independent set, ve-quasi isolated vertex, ve-dominating set