论文标题
在类似产品的图中定向统治
Orientable domination in product-like graphs
论文作者
论文摘要
图形$ g $的定向支配数字，$ {\ rm dom}（g）$是$ g $的所有方向的最大统治号码。在本文中，在不同的产品图和相关图形操作上研究了$ {\ rm dom} $。确定了任意电晕产品的可定向支配数量，而笛卡尔和词典产物则证明了尖锐的下限和上限。 Chartrand等人的结果。从1996年开始，通过建立$ {\ rm dom}的值（k_ {n_1，n_2，n_3}）$的$ {\ rm dom} $，用于任意正整数$ n_1，n_2 $和$ n_3 $。在考虑词素产品图的可定向支配数量时，我们在负面回答了一个有关[Digraphs及其直接和笛卡尔产品的统治及其直接挖掘物中的统治和包装数量的问题J. Graph Theory 99（2022）359-377]。
The orientable domination number, ${\rm DOM}(G)$, of a graph $G$ is the largest domination number over all orientations of $G$. In this paper, ${\rm DOM}$ is studied on different product graphs and related graph operations. The orientable domination number of arbitrary corona products is determined, while sharp lower and upper bounds are proved for Cartesian and lexicographic products. A result of Chartrand et al. from 1996 is extended by establishing the values of ${\rm DOM}(K_{n_1,n_2,n_3})$ for arbitrary positive integers $n_1,n_2$ and $n_3$. While considering the orientable domination number of lexicographic product graphs, we answer in the negative a question concerning domination and packing numbers in acyclic digraphs posed in [Domination in digraphs and their direct and Cartesian products, J. Graph Theory 99 (2022) 359-377].
