Signed total double Roman dominating functions in graphs

Abstract

A signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] 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 [Formula: see text] and (iii) [Formula: see text] holds for any vertex v. The weight of a STDRDF is the value [Formula: see text] The signed total double Roman domination number [Formula: see text] is the minimum weight of a STDRDF on G. In this article, we provide various bounds on [Formula: see text] and we show that the corresponding decision problem is NP-complete for bipartite and chordal graphs. In addition, we determine the signed total double Roman domination number of some classes of graphs including cycles, complete graphs and complete bipartite graphs.

Keywords

• Roman domination
• signed double Roman domination
• signed total double Roman domination
• 05C69
• 05C05