| 摘要: |
| 本文研究了直径为d(Γ) ≥ 2的距离正则图Γ的补图.利用Γ的交叉数分别证明了当d=2时,Γ的补图式强正则;当d ≥ 3时,Γ的补图是广义强正则.将文献[2]中的距离正则图Grassmann图、对偶极图、Hamming图推广到它们的补图,从而得到广义强正则图. |
| 关键词: 距离正则图 推广 强正则图 广义强正则图 |
| DOI： |
| 分类号:O157.5 |
| 基金项目:Supported by the Foundation of Langfang Teachers' College (LSLQ201504) |
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| COMPLEMENTS OF DISTANCE-REGULAR GRAPHS |
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ZHANG Xi-en, JIANG Wei
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School of Mathematics and Information Science, Langfang Teachers University, Langfang 065000, China
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| Abstract: |
| In this paper, we study the complement of Γ which is a distance-regular graph with diameter d(Γ) ≥ 2. By using intersection numbers of Γ, we show that the complement of Γ is strongly regular or generalized strongly regular as d=2 or d ≥ 3, respectively. We get the complements of Grassmann graph, dual polar graph and Hamming graph in [2], which are the generalized strongly regular. |
| Key words: distance-regular graph complement strongly regular graph generalized strongly regular graph |
