A characterization of $Q$-polynomial distance-regular graphs using the intersection numbers

Supalak Sumalroj

A characterization of $Q$-polynomial distance-regular graphs using the intersection numbers

Combinatorics 2017-06-13 v1

Authors: Supalak Sumalroj

Abstract

We consider a primitive distance-regular graph $\Gamma$ with diameter at least $3$ . We use the intersection numbers of $\Gamma$ to find a positive semidefinite matrix $G$ with integer entries. We show that $G$ has determinant zero if and only if $\Gamma$ is $Q$ -polynomial.

Keywords

graph theory of groups graph polynomials zero-divisor graphs

Cite

@article{arxiv.1706.03132,
  title  = {A characterization of $Q$-polynomial distance-regular graphs using the intersection numbers},
  author = {Supalak Sumalroj},
  journal= {arXiv preprint arXiv:1706.03132},
  year   = {2017}
}

Comments

15 pages

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