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Almost 2-Homogeneous Graphs and Completely Regular Quadrangles.
- Source :
-
Graphs & Combinatorics . Dec2008, Vol. 24 Issue 6, p571-585. 15p. - Publication Year :
- 2008
-
Abstract
- Many known distance-regular graphs have extra combinatorial regularities: One of them is t-homogeneity. A bipartite or almost bipartite distance-regular graph is 2-homogeneous if the number γ i = |{ x | ∂( u, x) = ∂( v, x) = 1 and ∂( w, x) = i − 1}| ( i = 2, 3,..., d) depends only on i whenever ∂( u, v) = 2 and ∂( u, w) = ∂( v, w) = i. K. Nomura gave a complete classification of bipartite and almost bipartite 2-homogeneous distance-regular graphs. In this paper, we generalize Nomura’s results by classifying 2-homogeneous triangle-free distance-regular graphs. As an application, we show that if Γ is a distance-regular graph of diameter at least four such that all quadrangles are completely regular then Γ is isomorphic to a binary Hamming graph, the folded graph of a binary Hamming graph or the coset graph of the extended binary Golay code of valency 24. We also consider the case Γ is a parallelogram-free distance-regular graph. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BIPARTITE graphs
*GRAPH theory
*COMBINATORIAL geometry
*DIAMETER
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 09110119
- Volume :
- 24
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Graphs & Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 35500393
- Full Text :
- https://doi.org/10.1007/s00373-008-0812-x