bounds on signed total double roman domination

A signed total double roman dominating function (stdrdf) on {an} isolated-free graph g=(v,e) is a function f:v(g)→{−1,1,2,3} such that (i) every vertex v with f(v)=−1 has at least two neighbors assigned 2 under f or one neighbor w with f(w)=3, (ii) every vertex v with f(v)=1 has at least one neighbor w with f(w)≥2 and (iii) ∑u∈n(v)f(u)≥1 holds for any vertex v. the weight of {an} stdrdf is the value f(v(g))=∑u∈v(g)f(u). the signed total double roman domination number γtsdr(g) is the minimum weight of an stdrdf on g. in this paper, we continue the study of the signed total double roman domination in graphs and present some sharp bounds for this parameter.