Nonexistence of graphs with cyclic defect (Q540060)
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scientific article; zbMATH DE number 5903001
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonexistence of graphs with cyclic defect |
scientific article; zbMATH DE number 5903001 |
Statements
Nonexistence of graphs with cyclic defect (English)
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1 June 2011
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Summary: We consider graphs of maximum degree \(\Delta \), diameter \(D\) and order \(M(\Delta , D) - 2\), where \(M(\Delta, D)\) is the Moore bound, that is, graphs of defect 2. \textit{C. Delorme} and \textit{G. Pineda-Villavicencio} [``On graphs with cyclic defect or excess,'' Electron. J. Comb. 17, No.\,1, Research Paper P143, 25 p., electronic only (2010; Zbl 1204.05043)] conjectured that such graphs do not exist for \(D \geq 3\) if they have the so called `cyclic defect'. Here we prove that this conjecture holds.
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graphs with cyclic defect
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Moore bound
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defect
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repeat
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