论文标题
关于巡回赛笛卡尔产物的条件连通性
On conditional connectivity of the Cartesian product of cycles
论文作者
论文摘要
The conditional $h$-vertex($h$-edge) connectivity of a connected graph $H$ of minimum degree $ k > h$ is the size of a smallest vertex(edge) set $F$ of $H$ such that $H - F$ is a disconnected graph of minimum degree at least $h.$ Let $G$ be the Cartesian product of $r\geq 1$ cycles, each of length at least four and let $h$ be an整数使得$ 0 \ leq H \ leq 2R-2 $。在本文中，我们确定了图$G。$g。$ $ h $ h $ vertex-connectivity和条件$ h $ - edge-g.-connectitive $g。$我们证明，这两种连接性均等于$（2r-h）a_h^r $，其中$ a_h^r $是$ a_h^r $，其中$ a_h^r $是最小的$ h $ h $ h $ groungular ungular of $ h $ grom-h $ grom-groumar of-groumar of $ h $ g. $ $ $ $ $。
The conditional $h$-vertex($h$-edge) connectivity of a connected graph $H$ of minimum degree $ k > h$ is the size of a smallest vertex(edge) set $F$ of $H$ such that $H - F$ is a disconnected graph of minimum degree at least $h.$ Let $G$ be the Cartesian product of $r\geq 1$ cycles, each of length at least four and let $h$ be an integer such that $0\leq h\leq 2r-2$. In this paper, we determine the conditional $h$-vertex-connectivity and the conditional $h$-edge-connectivity of the graph $G.$ We prove that both these connectivities are equal to $(2r-h)a_h^r$, where $a_h^r$ is the number of vertices of a smallest $h$-regular subgraph of $G.$
