Bounding the diameter of distance-regular graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1988 English Publisher:Springer Science and Business Media LLCJournal:Combinatorica, volume 8, pages 333-343 (issn: 0209-9683, eissn: 1439-6912,

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Authors: Chris D. Godsil;

doi: 10.1007/bf02189090

Bounding the diameter of distance-regular graphs

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Abstract

Let G be a connected distance regular graph with valence \(k>2\) and diameter d. Suppose further that G is not a complete multipartite graph. let \(\theta\) be an eigenvalue of G with \(\theta \neq Ik,\) and \(m>1\). Then there are only finitely many connected, co-connected distance regular graphs with an eigenvalue of multiplicity m.

Related Organizations

Simon Fraser University
Canada

Keywords

Graph theory, Graphs and linear algebra (matrices, eigenvalues, etc.), eigenvalue, connected graphs, co-connected graphs, distance regular graph, Paths and cycles

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