Signed Roman edge domination numbers in graphs

The closed neighborhood of an edge in a graph is the set consisting of and of all edges having a common end-vertex with . Let be a function on , the edge set of , into the set . If for every edge of and every edge for which is adjacent to at least one edge for which , then is called a signed Roman edge dominating function of . The minimum of the values , taken over all signed Roman edge dominating functions of , is called the signed Roman edge domination number of and is denoted by . In this note we initiate the study of the signed Roman edge domination in graphs and present some (sharp) bounds for this parameter.