# 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 {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) $\sum_{u\in N(v)}f(u)\ge1$ holds for any vertex $v$. The weight of {an} STDRDF is the value $f(V(G))=\sum_{u\in V(G)}f(u).$ The signed total double Roman domination number $\gamma^t_{sdR}(G)$ 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.

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