DOUBLE OUTER INDEPENDENT EDGE DOMINATION IN GRAPHS

Abstract

We introduce the concept of double outer independent edge domination in graph. The set  of edges of a graph, in which every edge of graphis dominated by at least two edges of , and the set of edges  is free means no two edges are adjacent, is called double outer independent edge dominating set of  a graph , represented by - set of . The least number of edges contained in this set is called - number of .  Initially, some straight forward and inequality results were given. Also we describe the result for extremal graphs. Further, the effect of deleting the edges is also discussed. At the end, Nordhaus – Gaddum type inequalities were obtained.