超连通图的充分条件
Let G be a connected graph. The connectivity κ(G) of a connected graph G is the least positive integer k such that there is F⊂V, | F | = k, and G—F is disconnected or is a trivial graph. If every minimum vertex cut isolates a vertex of G, a graph G is super connected or super-κ. Define the inverse d...
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| Published in | Zhejiang da xue xue bao. Journal of Zhejiang University. Sciences edition. Li xue ban Vol. 45; no. 4; pp. 391 - 393 |
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| Main Author | |
| Format | Journal Article |
| Language | Chinese |
| Published |
厦门理工学院应用数学学院,福建厦门,361024
01.07.2018
Zhejiang University Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1008-9497 |
| DOI | 10.3785/j.issn.1008-9497.2018.04.001 |
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| Abstract | Let G be a connected graph. The connectivity κ(G) of a connected graph G is the least positive integer k such that there is F⊂V, | F | = k, and G—F is disconnected or is a trivial graph. If every minimum vertex cut isolates a vertex of G, a graph G is super connected or super-κ. Define the inverse degree of a graph G with no isolated vertices as . In this paper,we show that let G be a connected graph with order n and minimum degree δ, if , then G is super-κ. |
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| AbstractList | O157.5; 设G是一个连通图.图的连通度κ(G)存在一个最小正整数k,使得F?V,|F|=k且G-F不连通或是一个平凡图.如果每一个最小点割都孤立G的一个点,则图G是超连通的或超-κ的.定义没有孤立点的图G的逆度为R(G)=(∑v∈V 1/d(v)).得到:设n阶连通图G,最小度为δ,若R(G)<1+(2/δ+1)+(n-2δ-1/(n-l)(n-3)),则G是超-κ的. Let G be a connected graph. The connectivity κ(G) of a connected graph G is the least positive integer k such that there is F⊂V, | F | = k, and G—F is disconnected or is a trivial graph. If every minimum vertex cut isolates a vertex of G, a graph G is super connected or super-κ. Define the inverse degree of a graph G with no isolated vertices as . In this paper,we show that let G be a connected graph with order n and minimum degree δ, if , then G is super-κ. |
| Author | 郭利涛 |
| AuthorAffiliation | 厦门理工学院应用数学学院,福建厦门,361024 |
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| Keywords | 超连通 逆度 连通度 |
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| Snippet | O157.5; 设G是一个连通图.图的连通度κ(G)存在一个最小正整数k,使得F?V,|F|=k且G-F不连通或是一个平凡图.如果每一个最小点割都孤立G的一个点,则图G是超连通的或超-κ的.定义没有孤立点的图G的逆度为R(G)=(∑v∈V... Let G be a connected graph. The connectivity κ(G) of a connected graph G is the least positive integer k such that there is F⊂V, | F | = k, and G—F is... |
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| StartPage | 391 |
| SubjectTerms | connectivity inverse degree super connected |
| Title | 超连通图的充分条件 |
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