On the signed Roman edge k-domination in graphs

Document Type : Original paper

Author

Department of Mathematics Payame Noor University I.R. Iran

Abstract

Let k≥1 be an integer, and G=(V,E) be a finite and simple graph. The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and all edges having a common end-vertex with e. A signed Roman edge k-dominating function (SREkDF) on a graph G is a function f:E→{−1,1,2} satisfying the conditions that (i) for every edge e of G, ∑x∈N[e]f(x)≥k and (ii) every edge e for which f(e)=−1 is adjacent to at least one edge e′ for which f(e′)=2. The minimum of the values ∑e∈Ef(e), taken over all signed Roman edge k-dominating functions f of G, is called the signed Roman edge k-domination number of G and is denoted by γsRk′(G). In this paper we establish some new bounds on the signed Roman edge k-domination number.

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References

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Communications in Combinatorics and Optimization
Volume 2, Issue 1
June 2017
Pages 57-64

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