Edge-distance-regular graphs are distance-regular
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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.
CitationCámara, M. [et al.]. Edge-distance-regular graphs are distance-regular. "Journal of combinatorial theory. Series A", 2013, vol. 120, núm. 5, p. 1057-1067.
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