Nonexistence of a class of distance-regular graphs

Yu Pei Huang, Yeh Jong Pan, Chih-wen Weng

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2 Scopus citations

Abstract

Let Γ denote a distance-regular graph with diameter D > 3 and intersection numbers a1 = 0; a2 6≠ 0, and c2 = 1. We show a connection between the d-bounded property and the nonexistence of parallelograms of any length up to d+1. Assume further that Γ is with classical parameters (D; b; α ß), Pan and Weng (2009) showed that (b; α; ß) = (-2;-2; ((-2)D+1-1)/3): Under the assumption D > 4, we exclude this class of graphs by an application of the above connection.

Original languageEnglish
JournalElectronic Journal of Combinatorics
Volume22
Issue number2
DOIs
StatePublished - 3 Jun 2015

Keywords

  • Classical parameters
  • D-bounded
  • Distance-regular graph
  • Parallelogram
  • Strongly closed subgraph

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