| 极大3限制边连通二部图的充分条件 |
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| 引用本文： | 张磊.极大3限制边连通二部图的充分条件[J].数学的实践与认识,2021(1):302-307. |
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| 作者姓名： | 张磊 |
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| 作者单位： | 1.晋中学院数学学院 |
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| 基金项目： | 2016年度晋中学院博士基金科研项目(bsjj2016202);晋中学院创客团队项目(jzxycktd2019023)。 |
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| 摘 要： | 设G=(V,E)是一个连通图.称一个边集合S■E是一个k限制边割,如果G-S的每个连通分支至少有k个顶点.称G的所有k限制边割中所含边数最少的边割的基数为G的k限制边连通度,记为λ_k(G).定义ξ_k(G)=min{X,■]:|X|=k,GX]连通,■=V(G)\X}.称图G是极大k限制边连通的,如果λ_k(G)=ξ_k(G).本文给出了围长为g>6的极大3限制边连通二部图的充分条件.
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| 关 键 词： | 互连网络 二部图 3限制边连通度 点集对 |
A Sufficient Condition for Maximally 3-restricted Edge-connected Bipartite Graphs |
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| ZHANG Lei.A Sufficient Condition for Maximally 3-restricted Edge-connected Bipartite Graphs[J].Mathematics in Practice and Theory,2021(1):302-307. |
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| Authors: | ZHANG Lei |
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| Institution: | (School of Mathematics,Jinzhong University,Jinzhong 030619,China) |
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| Abstract: | For a connected network G=(V,E),an edge set S■E is a k-restricted edge cut if G-S is disconnected and every component of G-S has at least k vertices.The k-restricted edge connectivity of G,denoted byλ_k(G),is defined as the cardinality of a minimum k-restricted edge cut.Letξ_k(G)=min{|X,Y]|:|X|=k,GX]is connected},where Y=V\X.A graph G is maximally k-restricted edge connected ifλ_k(G)=ξ_k(G).In this paper,a sufficient condition is presented for bipartite graphs with girth g>6 to be maximally 3-restricted edge connected. |
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| Keywords: | interconnection networks bipartite graphs 3-restricted edge connectivity set pairs of vertices |
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