Almost 2-homogeneous Bipartite Distance-regular Graphs

Curtin, Brian

doi:10.1006/eujc.2000.0399

Cited by 22 publications

(24 citation statements)

References 23 publications

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“…In this paper we give an algebraic description of the 1-homogeneous distance-regular graphs. Our results are similar to those appearing in [8] concerning the tight distance-regular graphs, similar to those appearing in [7] concerning the 2-homogeneous and almost 2-homogeneous bipartite distance-regular graphs, and similar to those in [9] for general graphs. 2-Homogeneous bipartite distanceregular graphs have been studied in [5,8,7,10,[21][22][23][24]28].…”

Section: Introductionsupporting

confidence: 89%

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1-homogeneous, pseudo-1-homogeneous, and 1-thin distance-regular graphs

Curtin

Nomura

2005

Journal of Combinatorial Theory, Series B

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Section: Introductionsupporting

confidence: 89%

“…The 1-thin distance-regular graphs have recently received some attention [25,26,27]. Some analogous results for bipartite graphs (those which are "2-thin") have been treated in [6,7]. It is natural to consider the 1-thin distance-regular graphs with few minimal left ideals of endpoint one.…”

Section: Introductionmentioning

confidence: 98%

1-homogeneous, pseudo-1-homogeneous, and 1-thin distance-regular graphs

Curtin

Nomura

2005

Journal of Combinatorial Theory, Series B

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“…This algebraic characterization is studied in greater detail for the 1-homogeneous distance-regular graphs in [6] and for the 2-homogeneous bipartite distance-regular graphs in [5].…”

Section: T-homogeneity and Triple Regularity Around A Vertexmentioning

confidence: 99%

Algebraic Characterizations of Graph Regularity Conditions

Curtin

2005

Des Codes Crypt

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“…, d − 2}. Almost 2-homogeneous graphs were introduced and studied by Curtin [4]. Observe that 1 = 1, so 1 exists for every distanceregular graph.…”

Section: Theoremmentioning

confidence: 98%

Triangle- and pentagon-free distance-regular graphs with an eigenvalue multiplicity equal to the valency

Jurišić

Koolen

Miklavič

2005

Journal of Combinatorial Theory, Series B

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We classify triangle-and pentagon-free distance-regular graphs with diameter d 2, valency k, and an eigenvalue multiplicity k. In particular, we prove that such a graph is isomorphic to a cycle, a k-cube, a complete bipartite graph minus a matching, a Hadamard graph, a distance-regular graph with intersection array {k, k − 1, k − c, c, 1; 1, c, k − c, k − 1, k}, where k = ( 2 + 3 + 1), c = ( + 1), ∈ N, or a folded k-cube, k odd and k 7. This is a generalization of the results of Nomura (J.Combin. Theory Ser. B 64 (1995) 300-313) and Yamazaki (J. Combin. Theory Ser. B 66 (1996) 34-37), where they classified bipartite distance-regular graphs with an eigenvalue multiplicity k and showed that all such graphs are 2-homogeneous.We also classify bipartite almost 2-homogeneous distance-regular graphs with diameter d 4. In particular, we prove that such a graph is either 2-homogeneous (and thus classified by Nomura and Yamazaki), or a folded k-cube for k even, or a generalized 2d-gon with order (1, k − 1).

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Almost 2-homogeneous Bipartite Distance-regular Graphs

Cited by 22 publications

References 23 publications

1-homogeneous, pseudo-1-homogeneous, and 1-thin distance-regular graphs

1-homogeneous, pseudo-1-homogeneous, and 1-thin distance-regular graphs

Algebraic Characterizations of Graph Regularity Conditions

Triangle- and pentagon-free distance-regular graphs with an eigenvalue multiplicity equal to the valency

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