Author/Authors :
Shahbazi, L Department of Mathematics - Azarbaijan Shahid Madani University, Tabriz, I.R. Iran , Abdollahzadeh Ahangar, H Department of Mathematics - Babol Noshirvani University of Technology, Shariati Ave., Babol, I.R. Iran , Khoeilar, R Department of Mathematics - Azarbaijan Shahid Madani University, Tabriz, I.R. Iran , Sheikholeslami, S.M Department of Mathematics - Azarbaijan Shahid Madani University, Tabriz, I.R. Iran
Abstract :
A signed total double Roman dominating function (STDRDF) on an isolated-free graph G = (V;E) is a function f : V (G) ! f 1; 1; 2; 3g 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) P u2N(v) f(u) ≥ 1 holds for any vertex v. The weight of
an STDRDF is the value f(V (G)) = P u2V (G) f(u): The signed total double Roman domination number tsdR(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.
