孤立韧度变量和分数(k,n)-临界图  

Isolated toughness variable and fractional(k,n)-critical graphs

作　　者：高炜[1] GAO Wei(School of Information Science and Technology,Yunnan Normal University,Kunming 650500,China)

机构地区：[1]云南师范大学信息学院,云南昆明650500

出　　处：《苏州科技大学学报（自然科学版）》2023年第2期20-26,共7页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(12161094)。

摘　　要：孤立韧度变量I′(G)是衡量网络健壮性的有效工具,定义|S|和i(G-S)-1的最小比值,其中S■V(G)满足i(G-S)>1。图G称为分数(k,n)-临界图,若从G中删除任意n个顶点,其剩余子图依然存在分数k-因子。文献[10]中得到分数k-因子存在性的紧I′(G)界。论文将文献[10]的结果推广到分数临界图,即:若δ(G)≥k+n且I′(G)>2k+n-1,则G是分数(k,n)-临界图,其中k≥2和n≥0是整数。Isolated toughness variable I′(G)is an effective measurement of network robustness,which defines by minimumratio of|S|and i(G-S)-1,where S■V(G)satisfyies i(G-S)>1.Graph G is a fractional(k,n)-critical graph,if any n vertices are removed from G,the resulting subgraphs still admit a fractional k-factor.Based on the findings of Reference[10],which obtained the tight I′(G)bound of existence of fractional k-factor,this study generalizes the result of it to fractional critical graphs:ifδ(G)≥k+n and I′(G)>2k+n-1,then G is a fractional(k,n)-critical graph,where k≥2 and n≥0 are integers.

关 键 词：图 孤立韧度变量 分数k-因子 分数(k n)-临界图 

分 类 号：O157.6[理学—数学]