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A signed (res. signed total) Roman dominating function, SRDF (res.STRDF) for short, of a graph G = (V; E) is a function f : V ! f??1; 1; 2g satisfying the conditions that (i)Σv2N[v]f(v) 1 (res.Σv2N(v)f(v) 1) for any v 2 V , where N[v] is the closed ne