Strong Efficient Edge Domination number of some graphs obtained by duplicating their elements - M.Annapoopathi, N.Meena (International Journal of Modern Agriculture, 2020)
Let be a simple graph. A subset S of E(G) is a strong (weak) efficient edge dominating set of G if │Ns[e] Ç S│ = 1 for all e Î E(G)(│Nw[e] Ç S│ = 1 for all e Î E(G)) where Ns(e) ={f / f Î E(G) & deg f ≥ deg e}(Nw(e) ={f / f Î E(G) & deg f ≤ deg e}) and Ns[e]=Ns(e) È{e}(Nw[e] = Nw(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.