罗马{2}在图和图产品中的统治

Faezeh Alizade, Hamid Reza Maimani, Leila Parsaei Majd, Mina Rajabi Parsa
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引用次数: 4

摘要

对于$n$阶的图$G=(V,E)$,一个罗马$\{2\}$支配函数$f:V\右移\{0,1,2\}$具有这样的性质:对于$f$中的每个顶点$ V\,当$f(V)=0$时,$ V$与$f$下一个赋值为$2$的顶点相邻,或者$ V$与$f$下一个赋值为$1$的顶点相邻。在本文中,我们将所有具有Roman $\{2\}$-支配数的图归为集合$\{2,3,4,n-2,n-1,n\}$。进一步,我们得到了一些图运算的Roman $\{2\}$-支配数的一些结果。
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Roman {2}-domination in Graphs and Graph Products
For a graph $G=(V,E)$ of order $n$, a Roman $\{2\}$-dominating function $f:V\rightarrow\{0,1,2\}$ has the property that for every vertex $v\in V$ with $f(v)=0$, either $v$ is adjacent to a vertex assigned $2$ under $f$, or $v$ is adjacent to least two vertices assigned $1$ under $f$. In this paper, we classify all graphs with Roman $\{2\}$-domination number belonging to the set $\{2,3,4,n-2,n-1,n\}$. Furthermore, we obtain some results about Roman $\{2\}$-domination number of some graph operations.
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CiteScore
0.90
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0.00%
发文量
20
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