Bounding the diameter of distance-regular graphs

Abstract

LetG be a connected distance-regular graph with valencyk>2 and diameterd, but not a complete multipartite graph. Suppose thatθ is an eigenvalue ofG with multiplicitym and thatθ≠±k. We prove that bothd andk are bounded by functions ofm. This implies that, ifm>1 is given, there are only finitely many connected, co-connected distance-regular graphs with an eigenvalue of multiplicitym.

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This work was supported by NSERC grant A5367.

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Godsil, C.D. Bounding the diameter of distance-regular graphs. Combinatorica 8, 333–343 (1988). https://doi.org/10.1007/BF02189090

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AMS subject classification code (1980)

  • 05 C 99