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Distance-Regular Graphs with an Eigenvalue of Multiplicity Four

✍ Scribed by R.R. Zhu

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 939 KB
Volume: 57
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1993.1014

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✦ Synopsis

Let (G) be a distance-regular graph. If (G) has an eigenvalue (\theta) of multiplicity (m) ((\geqslant 2)), then (G) has a natural representation in (R^{m}). By studying the geometric properties of the image configuration in (R^{m}), we can obtain considerable information about the graph-theoretic properties of (G) itself. This sets the basis for classifying distance-regular graphs by their eigenvalue multiplicities. It is known that the distance-regular graphs with an eigenvalue of multiplicity three are exactly the five Platonic solids plus all complete 4-partite regular graphs. In this paper we classify the distance-regular graphs with an eigenvalue of multiplicity four. 1993 Academic Press, Inc.

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