论文标题
$ g $ -Extra连接的强大路径和周期产物
The $g$-extra connectivity of the strong product of paths and cycles
论文作者
论文摘要
令$ g $为连接的图形，$ g $为非负整数。 $ g $ -EXTRA的连接$ g $是$ g $的一组顶点的最低基数，如果存在，它们的删除断开了$ g $，并且将每个组件都带有超过$ g $的顶点。强产品$ g_1 \ boxtimes g_2 g_2 $ g_1 =（v_ {1}，e_ {1}）$和$ g_2 =（v_ {2}，e_ {2}，e_ {2}）$是带有顶点的图形 $(x_{1}, x_{2}), (y_{1}, y_{2}) \in V_{1} \times V_{2}$ are adjacent in $G_1 \boxtimes G_2$ if and only if $x_{i}=y_{i}$ or $x_{i} y_{i} \in e_ {i} $ for $ i = 1，2 $。在本文中，我们获得了两条路径的强产物的$ g $ -Extra连接性，路径和周期的强产物以及两个循环的强产物。
Let $G$ be a connected graph and $g$ be a non-negative integer. The $g$-extra connectivity of $G$ is the minimum cardinality of a set of vertices in $G$, if it exists, whose removal disconnects $G$ and leaves every component with more than $g$ vertices. The strong product $G_1 \boxtimes G_2$ of graphs $G_1=(V_{1}, E_{1})$ and $G_2=(V_{2}, E_{2})$ is the graph with vertex set $V(G_1 \boxtimes G_2)=V_{1} \times V_{2}$, where two distinct vertices $(x_{1}, x_{2}), (y_{1}, y_{2}) \in V_{1} \times V_{2}$ are adjacent in $G_1 \boxtimes G_2$ if and only if $x_{i}=y_{i}$ or $x_{i} y_{i} \in E_{i}$ for $i=1, 2$. In this paper, we obtain the $g$-extra connectivity of the strong product of two paths, the strong product of a path and a cycle, and the strong product of two cycles.
