Signed Roman domination number in graphs

A signed Roman dominating function of G is afunction f: V (G) → {− 1, 1, 2} satisfying the conditions that(i)Σ(yϵN[x] f(y) ≥ 1 for each x ϵ V (G), where N[x] is theclosed neighborhood of x, (ii) every vertex x ϵ V (G) for whichf(x) = −1 is adjacent to at least one vertex y ϵV (G) for whichf(y) = 2. The weight of a signed Roman dominating functionf is ω(f) = Σ(xϵV (G) f(x). The signed Roman dominationnumber γsR(G) of G is the minimum weight of a signed Romandominating function of G. In this note we initiate the study ofsigned Roman domination in total graphs.