Distance-regular graphs with a 1 or c 2 at least half the valency

Jack H. Koolen, Jongyook Park

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

In this paper, we study the distance-regular graphs Γ that have a pair of distinct vertices, say x and y, such that the number of common neighbors of x and y is about half the valency of Γ. We show that if the diameter is at least three, then such a graph, besides a finite number of exceptions, is a Taylor graph, bipartite with diameter three or a line graph.

Original languageEnglish
Pages (from-to)546-555
Number of pages10
JournalJournal of Combinatorial Theory. Series A
Volume119
Issue number3
DOIs
StatePublished - Apr 2012

Keywords

  • Distance-regular graphs
  • Line graphs
  • Taylor graphs

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