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arXiv · 1210.5649

Edge-distance-regular graphs are distance-regular

M. Cámara·C. Dalfó·C. Delorme·M. A. Fiol·H. Suzuki
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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 $\G$ is distance-regular and homogeneous. More precisely, $\G$ 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.

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M. Cámara, C. Dalfó, C. Delorme, M. A. Fiol, H. Suzuki. 2012-10-20. Edge-distance-regular graphs are distance-regular. https://arxiv.org/abs/1210.5649

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