Signed Roman edge domination numbers in graphs

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