论文标题
有限基团的功率图的强度度尺寸
Strong metric dimensions for power graphs of finite groups
论文作者
论文摘要
令$ g $为有限的组。 $ g $的订单超图是带有顶点套装$ g $的图形，如果$ o（x）\ mid o（y）$（y）$或$ o（y）\ y（y）\ mid o（x）$，则两个不同的顶点$ x，y $相邻。 $ g $的增强功率图是其顶点集为$ g $的图形，如果它们生成环状亚组，则两个不同的顶点相邻。 $ g $的简化功率图是带顶点套装$ g $的图形，如果$ \ langle x \ rangle \ subset \ subset \ langle y \ y \ rangle $或$ \ langle y \ langle y \ y \ rangle y \ rangle \ subset \ subset \ subset \ subse \ langle x \ langle x \ rangle x \ rangle $。在本文中，我们表征了有限基团的阶级超图，增强功率图和还原功率图的强度度量。
Let $G$ be a finite group. The order supergraph of $G$ is the graph with vertex set $G$, and two distinct vertices $x,y$ are adjacent if $o(x)\mid o(y)$ or $o(y)\mid o(x)$. The enhanced power graph of $G$ is the graph whose vertex set is $G$, and two distinct vertices are adjacent if they generate a cyclic subgroup. The reduced power graph of $G$ is the graph with vertex set $G$, and two distinct vertices $x,y$ are adjacent if $\langle x\rangle \subset \langle y\rangle$ or $\langle y\rangle \subset \langle x\rangle$. In this paper, we characterize the strong metric dimension of the order supergraph, the enhanced power graph and the reduced power graph of a finite group.
