Partially metric association schemes with a multiplicity three
| Autor: | Jongyook Park, Edwin van Dam, Jack H. Koolen |
|---|---|
| Přispěvatelé: | Econometrics and Operations Research, Research Group: Operations Research |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
2-walk-regular graph
Symmetric graph 0211 other engineering and technologies 0102 computer and information sciences 02 engineering and technology 01 natural sciences Distance-regular graph Theoretical Computer Science association scheme Combinatorics distance-regular graph FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics small multiplicity Eigenvalues and eigenvectors Mathematics Discrete mathematics Foster graph Nauru graph 021107 urban & regional planning Symmetric relation Association scheme Computational Theory and Mathematics 010201 computation theory & mathematics Bipartite graph Combinatorics (math.CO) 05E30 05C50 cover of the cube |
| Zdroj: | Journal of Combinatorial Theory, Series B, Graph theory, 130, 19-48. Academic Press Inc. |
| ISSN: | 0095-8956 |
| Popis: | An association scheme is called partially metric if it has a connected relation whose distance-two relation is also a relation of the scheme. In this paper we determine the symmetric partially metric association schemes with a multiplicity three. Besides the association schemes related to regular complete $4$-partite graphs, we obtain the association schemes related to the Platonic solids, the bipartite double scheme of the dodecahedron, and three association schemes that are related to well-known $2$-arc-transitive covers of the cube: the M\"{o}bius-Kantor graph, the Nauru graph, and the Foster graph F048A. In order to obtain this result, we also determine the symmetric association schemes with a multiplicity three and a connected relation with valency three. Moreover, we construct an infinite family of cubic arc-transitive $2$-walk-regular graphs with an eigenvalue with multiplicity three that give rise to non-commutative association schemes with a symmetric relation of valency three and an eigenvalue with multiplicity three. Comment: 26 pages, 12 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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