Almost-bipartite distance-regular graphs with the $Q$-polynomial property

Michael S. Lang; Paul M. Terwilliger

Almost-bipartite distance-regular graphs with the $Q$-polynomial property

Combinatorics 2016-09-07 v1 Representation Theory

Authors: Michael S. Lang , Paul M. Terwilliger

Abstract

Let $G$ denote a $Q$ -polynomial distance-regular graph with diameter $D$ at least 4. Assume that the intersection numbers of $G$ satisfy $a_i=0$ for $0 \leq i \leq D-1$ and $a_D\neq 0$ . We show that $G$ is a polygon, a folded cube, or an Odd graph.

Keywords

bipartite graphs graph polynomials graph theory

Cite

@article{arxiv.math/0508435,
  title  = {Almost-bipartite distance-regular graphs with the $Q$-polynomial property},
  author = {Michael S. Lang and Paul M. Terwilliger},
  journal= {arXiv preprint arXiv:math/0508435},
  year   = {2016}
}

Comments

8 pages

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