| 一类无三角正则图的性质 |
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| 引用本文： | 费旭云,简芳洪. 一类无三角正则图的性质[J]. 阜阳师范学院学报(自然科学版), 2011, 28(1): 18-20 |
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| 作者姓名： | 费旭云 简芳洪 |
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| 作者单位： | 九江学院理学院,江西,九江,332005 |
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| 摘 要： | 图为无三角正则图,它满足不相邻的顶点恰有两个公共相邻顶点.先从代数的角度去研究它的特征值,得到了它的顶点个数只能取一些特殊的整数,然后证明了其点连通度与边连通度相等,而且存在完美匹配,最后猜想:(1)x(G)=x'(G)=k;(2)图G是Hamilton图.
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| 关 键 词： | 正则图 无三角图 邻接矩阵 图谱 |
Propositions of a triangle-free regular graph |
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| FEI Xu-yun,JIAN Fang-hong. Propositions of a triangle-free regular graph[J]. Journal of Fuyang Teachers College:Natural Science, 2011, 28(1): 18-20 |
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| Authors: | FEI Xu-yun JIAN Fang-hong |
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| Affiliation: | FEI Xu-yun,JIAN Fang-hong(College of Science,Jiujiang University,Jiangxi Jiujiang 332005,China) |
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| Abstract: | Grpah G is a triangle-free k-regular graph,and its two disadjacent vertices have just two common neighbours.First,its eigenvalues is studied,n the number of vertices of the graph must be some special integers.Then it is proved that its connectivity is equal to the edge-connectivity and it has perfect matching.At last,two conjectures are given ::(1) χ(G)=χ′(G)=k;(2)graph G is Hamilton. |
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| Keywords: | regular graphs triangle-free graphs adjacency matrix spectrum of graphs |
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