一类特殊图k-限制边连通度
k-Restricted Edge Connectivity of a Class of Special Graphs
石琳 1武彩萍 1杨卫华1
作者信息
- 1. 太原理工大学数学学院,山西太原 030024
- 折叠
摘要
设F⊆E(G)为图G=(V,E)的一个边集,如果G-F不连通且G-F的每一个连通分支都至少有k个顶点,F就称为图G的一个k-限制性边割.图G的k-限制边连通度是图G的最小k-限制性边割的基数,记为λk(G).限制性边连通度是衡量网络可靠性的重要参数之一.证明了在2 ≤k≤n,h ≤n/2的情况下,一类特殊图—蜻蜒网络D(n,h)的k-限制边连通度是λk(D(n,h))={nk-k2+kh,k≤h,nh,k＞h.
Abstract
Let F⊆E(G)be an edge set of the graph G=(V,E).If G-F is disconnected and ev-ery connected branch of G-F has at least k vertices,F is called a k-restricted edge cut of the graph G.The k-restricted edge connectivity of graph G,denoted as λk(G),is the cardinal number of the minimum k-restricted edge cut of graph G.The restricted edge connectivity is one of the important parameters to measure reliability of networks.The k-restricted edge connectivity of the dragonfly network D(n,h)is proved to be λk(D(n,h))={nk-k2+kh,k≤ h,nh,k＞h.
关键词
蜻蜒网/k-限制边连通度/网络Key words
dragonfly networks/k-restricted edge connectivity/networks引用本文复制引用
基金项目
山西省自然科学基金(20210302123097)
出版年
2024
NETL
NSTL
万方数据