Edge-distance-regular graphs are distance-regular
Edge-distance-regular graphs are distance-regular
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DOI：
10.1016/j.jcta.2013.02.006
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发表时间：
2012-10
期刊：
影响因子：
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通讯作者：
M. Cámara;C. Dalfó;C. Delorme;M. A. Fiol;H. Suzuki
中科院分区：
文献类型：
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作者：
M. Cámara;C. Dalfó;C. Delorme;M. A. Fiol;H. Suzuki
一个图是边距离正则的，当它的每条边都是距离正则的，并且它对任何以根为根的边都有相同的交数。本文给出了边距离正则图Γ是距离正则且齐次图的一些(组合的和代数的)证明。更准确地说，Γ是边距离正则的当且仅当它是二部距离正则或广义奇图。我们还得到了它们对应的一些参数之间的关系，主要是距离多项式和交数之间的关系。
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.