The h-faulty-block connectivity of alternating group graphs and split-star networks

期刊论文
发表日期：

2024年6月19日

查看全文

Xiaohui Hua,
Qin Zhao

摘要

The connectivity of a network is an important indicator for assessing its reliability and fault-tolerability. In this paper, we study a novel measurement, which is the h-faulty-block connectivity. Given a connected graph G and a nonnegative integer h, let $C\subset V(G)$ $C \subset V (G)$ and G[C] be a connected subgraph. Then, C is called an h-faulty-block of G if $G-C$ $G - C$ is disconnected, and every remaining component of $G-C$ $G - C$ has at least $h+1$ $h + 1$ nodes. The minimum cardinality over all h-faulty-blocks of G is called h-faulty-block connectivity of G, denoted by $FB_{k_h}(G)$ $F B_{k_{h}} (G)$ . In this paper, we focus on the alternating group graphs and split-star networks. We study the $\{0, 1, 2\}$ ${0, 1, 2}$ -faulty-block connectivity of the two kinds of graphs and show that $FB_{k_0}(AG_n)=3n-7$ $F B_{k_{0}} (A G_{n}) = 3 n - 7$ for $n\ge 4$ $n \geq 4$ , $FB_{k_1}(AG_n)=5n-14$ $F B_{k_{1}} (A G_{n}) = 5 n - 14$ for $n\ge 5$ $n \geq 5$ , $FB_{k_2}(AG_n)=7n-22$ $F B_{k_{2}} (A G_{n}) = 7 n - 22$ for $n\ge 6$ $n \geq 6$ , and $FB_{k_0}(S_n^2)=3n-5$ $F B_{k_{0}} (S_{n}^{2}) = 3 n - 5$ for $n\ge 4$ $n \geq 4$ , $FB_{k_1}(S_n^2)=5n-11$ $F B_{k_{1}} (S_{n}^{2}) = 5 n - 11$ for $n\ge 5$ $n \geq 5$ , $FB_{k_2}(S_n^2)=7n-18$ $F B_{k_{2}} (S_{n}^{2}) = 7 n - 18$ for $n\ge 6$ $n \geq 6$ .