The Algebraic and Vertex Connectivity of Graphs
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摘要: G是一个简单图.a(G),k(G)分别为G的代数连通度和点连通度,该文刻画了满足a(G)=k(G)的图.G=(V,E)是一个n阶简单图,点连通度为k(G)≤[n/2].H是G的任意最小点割集,则a(G)=k(G)当且仅当对任意u∈H和v∈V\H,有uv∈E.Abstract: G is a simple graph with a(G) and k(G), its algebraic and vertex connectivity.This paper finds all the graphs satisfying a(G)=k(G).G=(V,E) is a simple graph of order n with vertex connectivity k(G)≤[n/2],and H is one of G's minimal vertex cut set,then a(G)=k(G) holds if and only if for every u∈H and every v∈V\H, uv∈E.
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