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Erschienen in:
01.01.2016
Signed Roman edge domination numbers in graphs
Erschienen in: Journal of Combinatorial Optimization | Ausgabe 1/2016
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Abstract
The closed neighborhood \(N_G[e]\) of an edge \(e\) in a graph \(G\) is the set consisting of \(e\) and of all edges having a common end-vertex with \(e\). Let \(f\) be a function on \(E(G)\), the edge set of \(G\), into the set \(\{-1, 1, 2\}\). If \( \sum _{x\in N[e]}f(x) \ge 1\) for every edge \(e\) of \(G\) and every edge \(e\) for which \(f (e) = -1\) is adjacent to at least one edge \(e'\) for which \(f (e')= 2\), then \(f\) is called a signed Roman edge dominating function of \(G\). The minimum of the values \(\sum _{e\in E(G)} f(e)\), taken over all signed Roman edge dominating functions \(f\) of \(G\), is called the signed Roman edge domination number of \(G\) and is denoted by \(\gamma _{sR}'(G)\). In this note we initiate the study of the signed Roman edge domination in graphs and present some (sharp) bounds for this parameter.