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.
| Original language | English |
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| Pages (from-to) | 1057-1067 |
| Journal | Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics |
| Volume | 120 |
| Issue number | 5 |
| Publication status | Published - 2013 |