Edge-distance-regular graphs are distance-regular
Combinatorics
2012-10-23 v1
Abstract
A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph is distance-regular and homogeneous. More precisely, is edge-distance-regular if and only if it is bipartite distance-regular or a generalized odd graph. Also, we obtain the relationships between some of their corresponding parameters, mainly, the distance polynomials and the intersection numbers.
Cite
@article{arxiv.1210.5649,
title = {Edge-distance-regular graphs are distance-regular},
author = {M. Cámara and C. Dalfó and C. Delorme and M. A. Fiol and H. Suzuki},
journal= {arXiv preprint arXiv:1210.5649},
year = {2012}
}