English

Distance-regular graphs with exactly one positive $q$-distance eigenvalue

Combinatorics 2023-05-25 v1

Abstract

In this paper, we study the qq-distance matrix for a distance-regular graph and show that the qq-distance matrix of a distance-regular graph with classical parameters (D,q,α,βD, q, \alpha, \beta) has exactly three distinct eigenvalues, of which one is zero. Moreover, we study distance-regular graphs whose qq-distance matrix has exactly one positive eigenvalue.

Cite

@article{arxiv.2305.14636,
  title  = {Distance-regular graphs with exactly one positive $q$-distance eigenvalue},
  author = {Jack H. Koolen and Mamoon Abdullah and Brhane Gebremichel and Sakander Hayat},
  journal= {arXiv preprint arXiv:2305.14636},
  year   = {2023}
}

Comments

19 pages

R2 v1 2026-06-28T10:43:51.437Z