1403/01/09
دوستعلی مژده

دوستعلی مژده

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

مشخصات پژوهش

عنوان
Roman {3}-domination (double Italian domination)
نوع پژوهش
JournalPaper
کلیدواژه‌ها
(Roman, Roman {2}, double roman), domination, Roman {3}-domination
سال
2020
مجله DISCRETE APPLIED MATHEMATICS
شناسه DOI
پژوهشگران Doost Ali Mojdeh ، Lutz Volkmann

چکیده

For a graph $G = (V, E)$ with $V=V(G)$ and $E=E(G)$, a Roman $\{3\}$-dominating function is a function $f : V \rightarrow \{0, 1, 2, 3\}$ having the property that $\sum_{u\in N_G(v)} f(u)\ge 3$, if $f (v) = 0$, and $\sum_{u\in N_G(v)} f(u)\ge 2$, if $f (v) = 1$ for any vertex $v\in G$. The weight of a Roman $\{3\}$-dominating function $f$ is the sum $f (V) =\sum_{v\in V(G)} f(v)$ and the minimum weight of a Roman $\{3\}$-dominating function on $G$ is the Roman $\{3\}$-domination number of $G$, denoted by $\gamma_{\{R3\}}(G)$. We initiate the study of Roman $\{3\}$-domination and show its relationship to domination, Roman domination, Roman $\{2\}$-domination (Italian domination) and double Roman domination. Finally, we present an upper bound on the Roman $\{3\}$-domination number of a connected graph $G$ in terms of the order of $G$ and characterize the graphs attaining this bound. Finally, we show that associated decision problem for Roman $\{3\}$-domination is $NP$-complete, even for bipartite graphs.