Abstract

Let 𝐺 = (𝑉, 𝐸) be a simple graph. A subset S of E(G) is a strong (weak) efficient edge dominating set of G if │Ns[e]S│ = 1 for all eE(G) [│Nw[e]S│ = 1 for all e  E(G)] where Ns(e) ={f / f  E(G) & deg f ≥ deg e}[Nw (e) ={f / f  E(G) & deg f ≤ deg e}] and Ns[e]=Ns(e) {e}[Nw[e] = Nw (e) {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 𝛾′ 𝑠𝑒 (𝐺) [𝛾 ′ 𝑤𝑒 (𝐺)]. In this paper, the strong efficient edge domination number of some cycle related graphs are studied.

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References

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