Edge-distance-regular graphs are distance-regular
Camara,M. Dalfo,C. Delorme,C. Fiol,M.A. Suzuki,H.
Camara,M.
Dalfo,C.
Delorme,C.
Fiol,M.A.
Suzuki,H.
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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 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.
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2013
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Camara, M, Dalfo, C, Delorme, C, Fiol, M A & Suzuki, H 2013, 'Edge-distance-regular graphs are distance-regular', Journal of Combinatorial Theory Series A, vol. 120, no. 5, pp. 1057-1067.