Signed total double Roman k-domination in graphs

Abstract

A signed total double Roman [Formula: see text]-dominating function (STDRkDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text] has at least two neighbors assigned 2 under [Formula: see text] or at least one neighbor [Formula: see text] with [Formula: see text], (ii) every vertex [Formula: see text] with [Formula: see text] has at least one neighbor [Formula: see text] with [Formula: see text] and (iii) [Formula: see text] holds for any vertex [Formula: see text]. The weight of an STDRkDF is the value [Formula: see text] The signed total double Roman [Formula: see text]-domination number [Formula: see text] is the minimum weight among all STDRkDFs on [Formula: see text]. In this paper, we initiate the study of the signed total double Roman [Formula: see text]-domination in graphs and present some sharp bounds for this parameter. In addition, we determine the signed total double Roman [Formula: see text]-domination of paths for [Formula: see text].