An eigenvalue characterization of antipodal distance-regular graphs (Q1378523)
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scientific article; zbMATH DE number 1118014
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An eigenvalue characterization of antipodal distance-regular graphs |
scientific article; zbMATH DE number 1118014 |
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An eigenvalue characterization of antipodal distance-regular graphs (English)
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15 February 1998
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Summary: Let \(\Gamma\) be a regular (connected) graph with \(n\) vertices and \(d+1\) distinct eigenvalues. As a main result, it is shown that \(\Gamma\) is an \(r\)-antipodal distance-regular graph if and only if the distance graph \(\Gamma_d\) is constituted by disjoint copies of the complete graph \(K_r\), with \(r\) satisfying an expression in terms of \(n\) and the distinct eigenvalues.
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