Strong Efficient Edge Domination Number of Some Cycle Related Graphs

M.Annapoopathi; N.Meena

doi:https://doi.org/10.14445/22315373/IJMTT-V59P530

International Journal of Mathematics Trends and Technology

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Volume 59 | Number 3 | Year 2018 | Article Id. IJMTT-V59P530 | DOI : https://doi.org/10.14445/22315373/IJMTT-V59P530

Strong Efficient Edge Domination Number of Some Cycle Related Graphs

M.Annapoopathi, N.Meena

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.

Keywords

Domination, edge domination, strong edge domination, efficient edge domination, strong efficient edge domination.

References

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Citation :

M.Annapoopathi, N.Meena, "Strong Efficient Edge Domination Number of Some Cycle Related Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 59, no. 3, pp. 202-208, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V59P530