# Edge-distance-regular graphs are distance-regular

M. Camara, C. Dalfo, C. Delorme, M.A. Fiol, H. Suzuki

Research output: Contribution to journalArticleScientificpeer-review

### 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 1057-1067 Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics 120 5 Published - 2013

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Distance-regular Graph
Intersection number
Polynomials
Graph in graph theory
Odd
Roots
If and only if
Polynomial

### Cite this

Camara, M. ; Dalfo, C. ; Delorme, C. ; Fiol, M.A. ; Suzuki, H. / Edge-distance-regular graphs are distance-regular. In: Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics. 2013 ; Vol. 120, No. 5. pp. 1057-1067.
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title = "Edge-distance-regular graphs are distance-regular",
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.",
author = "M. Camara and C. Dalfo and C. Delorme and M.A. Fiol and H. Suzuki",
year = "2013",
language = "English",
volume = "120",
pages = "1057--1067",
journal = "Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics",
issn = "0097-3165",
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Camara, M, Dalfo, C, Delorme, C, Fiol, MA & Suzuki, H 2013, 'Edge-distance-regular graphs are distance-regular', 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.

In: Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics, Vol. 120, No. 5, 2013, p. 1057-1067.

Research output: Contribution to journalArticleScientificpeer-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 -