Twin signed double Roman domination numbers in directed graphs

Abstract

Let [Formula: see text] be a finite simple directed graph (shortly digraph). A function [Formula: see text] is called a twin signed double Roman dominating function (TSDRDF) if (i) every vertex [Formula: see text] with [Formula: see text] has at least two in-neighbor assigned a 2 or at least an in-neighbor [Formula: see text] with [Formula: see text], also at least two out-neighbor assigned a 2 or at least an out-neighbor [Formula: see text] with [Formula: see text] (ii) every vertex [Formula: see text] with [Formula: see text] is adjacent to at least an in-neighbor and an out-neighbor [Formula: see text] with [Formula: see text] and (iii) [Formula: see text] and [Formula: see text] hold for any vertex [Formula: see text]. The weight of a TSDRDF [Formula: see text] is [Formula: see text], the twin signed double Roman domination number [Formula: see text] of [Formula: see text] is the minimum weight of a TSDRDF on [Formula: see text]. In this paper, we initiate the study of twin signed double Roman domination in digraphs and we present some bounds for [Formula: see text].