### Abstract

Original language | English |
---|---|

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 |

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*Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics*,

*120*(5), 1057-1067.

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*Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics*, vol. 120, no. 5, pp. 1057-1067.

**Edge-distance-regular graphs are distance-regular.** / Camara, M.; Dalfo, C.; Delorme, C.; Fiol, M.A.; Suzuki, H.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Edge-distance-regular graphs are distance-regular

AU - Camara, M.

AU - Dalfo, C.

AU - Delorme, C.

AU - Fiol, M.A.

AU - Suzuki, H.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

M3 - Article

VL - 120

SP - 1057

EP - 1067

JO - Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics

JF - Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics

SN - 0097-3165

IS - 5

ER -