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Cámara, M.; Dalfó, C.; Delorme, C.; Fiol, M.A.; Suzuki, H.
Journal of combinatorial theory. Series A, 07/2013, Letnik: 120, Številka: 5Journal Article, Publication
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 Γ is distance-regular and homogeneous. More precisely, Γ 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.
