| Kronecker乘积图的超连通性(英文) |
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| 引用本文： | 郝琛,林辉球,覃城阜.Kronecker乘积图的超连通性(英文)[J].数学研究,2013(3):253-259. |
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| 作者姓名： | 郝琛 林辉球 覃城阜 |
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| 作者单位： | [1]晋中职业技术学院,山西晋中030600 [2]华东师范大学数学科学学院,上海200062 [3]广西师范学院数学科学学院,广西南宁530001 |
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| 基金项目： | The work was supported by NSFC （ 11171279, 1161006）, Natural Sciences Foundation of Guangxi Province （2012GXNSFBA053005）, the Scientific Research Foundation of Guangxi Education Committee （200103YB069） |
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| 摘 要： | 设G1和G2是两个连通图,则G1和G2的Kronecker积G1×G2定义如下:V(G1×G2)=V(G1)×V(G2),E(G1×G2)={(u1,v1)(u2,v2):u1u2∈E(G1),v1v2∈E(G2)}.我们证明了G×Kn(n≥4)超连通图当且仅当κ(G)n>δ(G)(n 1),其中G是任意的连通图,Kn是n阶完全图.进一步我们证明了对任意阶至少为3的连通图G,如果κ(G)=δ(G),则G×Kn(n≥3)超连通图.这个结果加强了郭利涛等人的结果.
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| 关 键 词： | Kronecker积 连通性 超连通性 |
A Note on the Super Connectivity of Kronecker Product of Graphs |
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| Hao Chen Lin Huiqiu Qin Chengfu.A Note on the Super Connectivity of Kronecker Product of Graphs[J].Journal of Mathematical Study,2013(3):253-259. |
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| Authors: | Hao Chen Lin Huiqiu Qin Chengfu |
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| Institution: | Hao Chen Lin Huiqiu Qin Chengfu ( 1. Jinzhong Vocational and Technical College, Jinzhong Slianxi 030600; 2. Department of Mathematics, East China Normal University, Shanghai 200062; 3. Department of Mathematics, Guang：xi Teachers Education University, Nanning Guangxi, 530001) |
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| Abstract: | Let G1 and G2 be two connected graphs. The Kronecker product G1 × G2 is the graph with vertex set V（G1 × G2） =V（G1） x V（G2） and the edge set E（G1 × G2） = （（ul,vl）（u2,u2） ： ulu2 ∈ E（G1）,ulu2 ∈ E（G2））. In this note, we show that G × Kn （n 〉 4） is super-k if and only if k（G）n 〉 δ（G）（n - 1）, where G is any connected graph and K,, is the complete of n vertices. Furthermore, we show that for any connected graph G with at least three vertices, if s（G） = 5（G） then G × Kn is super-k for n 〉 3. This result strengthens the known results of Guo et al.. |
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| Keywords: | Kronecker product Connectivity Super connectivity |
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