Edge-distance-regular graphs are distance-regular

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

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)1057-1067
JournalJournal of Combinatorial Theory, Series A, Structures designs and application combinatorics
Volume120
Issue number5
Publication statusPublished - 2013

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