论文标题
家庭常规网络的广义3连接性
The generalized 3-connectivity of a family regular networks
论文作者
论文摘要
图形$ g $的广义$ k $ - 连接性，用$κ_k（g）$表示，是任何$ s \ subseteq v（g）$ at $ | s | = k $的内部边缘分离$ s $ s $ s $ s $ s $。广义$ k $ - 连接性是经典连接性的自然扩展，并且在与现代互连网络相关的应用中起关键作用。在本文中，我们首先介绍了一个普通网络$ h_n $的家族，可以从几个子图$ g_n^1，g_n^2，\ cdots，g_n^{t_n} $中获得，每个子级$ g_n^i $ isomorphic is isomorphic is isomorphic is ismomorphic is ismomorphic is ismomorphic is iSomorphic is iSomorphic is isom g_n $ g_n $ g_n $ 1 $ 1 $ 1 $ 1.然后，我们确定$ h_n $的广义3连接性。作为主要结果的应用，某些两级互连网络的广义三连通性，例如层次星形图$ HS_N $，层次立方网络$ HCN_N $和层次折叠的Hypercube $ HFQ_N $。
The generalized $k$-connectivity of a graph $G$, denoted by $κ_k(G)$, is the minimum number of internally edge disjoint $S$-trees for any $S\subseteq V(G)$ with $|S|=k$. The generalized $k$-connectivity is a natural extension of the classical connectivity and plays a key role in applications related to the modern interconnection networks. In this paper, we firstly introduce a family of regular networks $H_n$ that can be obtained from several subgraphs $G_n^1, G_n^2, \cdots, G_n^{t_n}$ by adding a matching, where each subgraph $G_n^i$ is isomorphic to a particular graph $G_n$ ($1\le i\le t_n$). Then we determine the generalized 3-connectivity of $H_n$. As applications of the main result, the generalized 3-connectivity of some two-level interconnection networks, such as the hierarchical star graph $HS_n$, the hierarchical cubic network $HCN_n$ and the hierarchical folded hypercube $HFQ_n$, are determined directly.
