International Journal of Foundations of Computer Science ( IF 0.523 ) Pub Date : 2021-01-04 , DOI: 10.1142/s0129054121500088
Yuxing Yang

Let $G$ be an undirected graph. An $H$-structure-cut (resp. $H$-substructure-cut) of $G$ is a set of subgraphs of $G$, if any, whose deletion disconnects $G$, where the subgraphs deleted are isomorphic to a certain graph $H$ (resp. where for any $T′$ of the subgraphs deleted, there is a subgraph $T$ of $G$, isomorphic to $H$, such that $T′$ is a subgraph of $T$). $G$ is super$H|M$-connected (resp. super sub-$H|M$-connected) if the deletion of an arbitrary minimum $H$-structure-cut (resp. minimum $H$-substructure-cut) isolates a component isomorphic to a certain graph $M$. The $k$-ary $n$-cube $Qnk$ is one of the most attractive interconnection networks for multiprocessor systems. In this paper, we prove that $Qnk$ with $n≥3$ is super sub-$Ck|K1$-connected if $k≥3$ and $k$ is odd, and super $Ck|Ck$-connected if $k≥5$ and $k$ is odd.

k-Ary n-Cube网络的Super Ck和Sub-Ck连接

$G$是无向图。一个$H$-结构切割（resp。$H$-substructure-cut$G$ 是一组子图 $G$，如果有的话，其删除将断开 $G$，其中删除的子图与某个图是同构的 $H$ （分别代表哪里 $Ť′$ 在删除的子图中，有一个子图 $Ť$$G$，同构为 $H$，这样 $Ť′$ 是的子图 $Ť$）。 $G$$H|中号$-已连接（分别是超级子-$H|中号$-connected），如果删除任意最小值$H$-结构切割（分别为最小值 $H$-substructure-cut）将同构的组件隔离到某个图 $中号$。这$ķ$-ary $ñ$-立方体 $问ñķ$是多处理器系统最吸引人的互连网络之一。在本文中，我们证明$问ñķ$$ñ≥3$ 是超级子$Cķ|ķ1个$-如果连接 $ķ≥3$$ķ$ 奇怪，超级 $Cķ|Cķ$-如果连接 $ķ≥5$$ķ$ 很奇怪

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