Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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with r an integer and r greater-or-equal, slanted

1. Both cases serve to illustrate a technique which can help in determining structural properties for distance-regular graphs and association schemes with a sufficient number of vanishing Krein parameters.

Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs

Authors:	Kris Coolsaet Aleksandar Juri&#x;i&#x;

Institution:	^aDepartment of Applied Mathematics and Computer Science, Ghent University, 9000 Gent, Belgium;^bFaculty of Computer and Information Science and IMFM University of Ljubljana, 1000 Ljubljana, Slovenia

Abstract:	We prove the nonexistence of a distance-regular graph with intersection array {74,54,15;1,9,60} and of distance-regular graphs with intersection arrays {4r³+8r²+6r+1,2r(r+1)(2r+1),2r²+2r+1;1,2r(r+1),(2r+1)(2r²+2r+1)}

Keywords:	Krein parameters Association scheme Distance-regular graph Strongly regular graph Triple intersection numbers
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