• EDGE ENTIRE DOMINATION IN GRAPHS

Abstract

Let G= (V, E) be a graph. The vertices and edges of G are called the elements of G. Given elements x and y, we say x dominates y if x = y or if x and y are adjacent or incident. Thus an edge e of G dominates itself, the two end vertices of e and all edges incident to e. A set F Í E is an edge entire dominating set of G, if each element in G is dominated by some edge in F. The edge entire domination number gee(G) is the minimum cardinality of an edge entire dominating set of G. In this paper, we present some bounds on gee(G) and obtain exact values of gee(G) for some standard graphs. Also a Nordhaus-Gaddum type result is established.