Distance-regular graphs with \(b_ t=1\) and antipodal double-covers (Q1924148)
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scientific article; zbMATH DE number 934815
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distance-regular graphs with \(b_ t=1\) and antipodal double-covers |
scientific article; zbMATH DE number 934815 |
Statements
Distance-regular graphs with \(b_ t=1\) and antipodal double-covers (English)
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3 December 1996
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Let \(\Gamma\) be a distance-regular graph of diameter \(d\) and valency \(k>2\). If \(b_t=1\) and \(2t\leq d\), then \(\Gamma\) is an antipodal double-cover. Consequently, if \(f>2\) is the multiplicity of an eigenvalue of the adjacency matrix of \(\Gamma\) and if \(\Gamma\) is not an antipodal double-cover then \(d\leq 2f-3\). This result is an improvement of Godsil's bound.
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distance
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strongly regular graph
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distance-regular graph
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diameter
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antipodal double-cover
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eigenvalue
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adjacency matrix
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