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دوستعلی مژده

دوستعلی مژده

مرتبه علمی: استاد
ارکید:
تحصیلات: دکترای تخصصی
اسکاپوس:
دانشکده: دانشکده علوم ریاضی
نشانی:
تلفن: 011-35302448

مشخصات پژوهش

عنوان
Unique response strong Roman dominating functions of graphs
نوع پژوهش
JournalPaper
کلیدواژه‌ها
strong Roman dominating function, unique response strong Roman (dominating) function
سال
2021
مجله Electronic Journal of Graph Theory and Applications
شناسه DOI
پژوهشگران Doost Ali Mojdeh ، Guoliang Hao ، Iman Masoumi ، Ali Parsian

چکیده

Given a simple graph $G=(V,E)$ with maximum degree $\Delta$. Let $(V_{0},V_{1},V_{2})$ be an ordered partition of $V$, where $V_{i}=\{v\in V:f(v)=i\}$ for $i=0,1$ and $V_{2}=\{v\in V:f(v)\geq2\}$. A function $f:V\rightarrow\{0,1,...,\lceil\frac{\Delta}{2}\rceil+1\}$ is a strong Roman dominating function (StRDF) on $G$, if every $v\in V_{0}$ has a neighbor $w\in V_{2}$ and $f(w)\geq1+\lceil\frac{1}{2}|N(w)\cap V_{0}|\rceil $. A function $f:V\rightarrow\{0,1,...,\lceil\frac{\Delta}{2}\rceil+1\}$ is a unique response strong Roman function (URStRF), if $w\in V_{0}$, then $|N(w)\cap V_{2}|\leq1$ and $w\in V_{1}\cup V_{2}$ implies that $|N(w)\cap V_{2}|=0$. A function $f:V\rightarrow\{0,1,...,\lceil\frac{\Delta}{2}\rceil+1\}$ is a unique response strong Roman dominating function (URStRDF) if it is both URStRF and StRDF. The unique response strong Roman domination number of $G$, denoted by $u_{StR}% (G)$, is the minimum weight of a unique response strong Roman dominating function. In this paper we approach the problem of a Roman domination-type defensive strategy under multiple simultaneous attacks and begin with the study of several mathematical properties of this invariant. We obtain several bounds on such a parameter and give some realizability results for it. Moreover, for any tree $T$ of order $n\ge 3$ we prove the sharp bound $u_{StR}(T)\leq\frac {8n}{9}$.