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Bounds on signed total double Roman domination | ||
| Communications in Combinatorics and Optimization | ||
| دوره 5، شماره 2، اسفند 2020، صفحه 191-206 اصل مقاله (390.25 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2020.26761.1140 | ||
| نویسندگان | ||
| L. Shahbazi1؛ H. Abdollahzadeh Ahangar* 2؛ R. Khoeilar1؛ Seyed Mahmoud Sheikholeslami1 | ||
| 1Azarbaijan Shahid Madani University | ||
| 2Babol Noshirvani University of Technology | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Roman domination؛ signed double Roman domination؛ signed total double Roman domination | ||
| مراجع | ||
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