Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21285220201201Bounds on signed total double Roman domination1912061406110.22049/cco.2020.26761.1140ENL.ShahbaziAzarbaijan Shahid Madani UniversityH.Abdollahzadeh AhangarBabol Noshirvani University of Technology0000-0002-0038-8047RanaKhoeilarAzarbaijan Shahid Madani University0000-0002-2981-3625Seyed MahmoudSheikholeslamiAzarbaijan Shahid Madani University0000-0003-2298-4744Journal Article20200207A signed total double Roman dominating function (STDRDF) on {color{blue}an} isolated-free graph $G=(V,E)$ is a<br />function $f:V(G)rightarrow{-1,1,2,3}$ such that (i) every vertex $v$ with $f(v)=-1$ has at least two<br />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)<br />$sum_{uin N(v)}f(u)ge1$ holds for any vertex $v$.<br />The weight of {color{blue}an} STDRDF is the value $f(V(G))=sum_{uin V(G)}f(u).$ The signed total<br />double Roman domination number $gamma^t_{sdR}(G)$ is the minimum weight of {color{blue}an}<br />STDRDF on $G$. In this paper, we continue the study of the signed total double Roman<br />domination in graphs and present some sharp bounds for this parameter.http://comb-opt.azaruniv.ac.ir/article_14061_e11b84bc918c5f13db5dfa4080bc9852.pdf