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Abstract
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The closed neighborhood NG[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 x∈N[e] f (x) ≥ 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 e∈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 γ 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.
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