Strong Efficient Edge Domination number of some graphs obtained by duplicating their elements

Abstract

Let  be a simple graph. A subset S of E(G) is a strong (weak) efficient edge dominating set of G if │N_s[e] Ç S│ = 1 for all e Î E(G)(│N_w[e] Ç S│ = 1 for all e Î E(G)) where N_s(e) ={f / f Î E(G) & deg f ≥ deg e}(N_w(e) ={f / f Î E(G) & deg f ≤ deg e}) and N_s[e]=N_s(e) È{e}(N_w[e] = N_w(e) È{e}). The minimum cardinality of a strong efficient edge dominating set of G (weak efficient edge dominating set of G) is called a strong efficient edge domination number of G and is denoted by  ( . In this paper, the strong efficient edge domination number of some graphs obtained by duplicating their elements is studied.