Bounds on signed total double Roman domination

Document Type: Original paper

Authors

1 Azarbaijan Shahid Madani University

2 Babol Noshirvani University of Technology

Abstract

A signed total double Roman dominating function (STDRDF) on {color{blue}an} isolated-free graph $G=(V,E)$ is a
function $f:V(G)rightarrow{-1,1,2,3}$ 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 $f(w)geq2$ and (iii)
$sum_{uin N(v)}f(u)ge1$ holds for any vertex $v$.
The weight of {color{blue}an} STDRDF is the value $f(V(G))=sum_{uin V(G)}f(u).$ The signed total
double Roman domination number $gamma^t_{sdR}(G)$ is the minimum weight of {color{blue}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.

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