On graphs with just three distinct eigenvalues
| Autor: | Rowlinson, Peter |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Factor-critical graph
Vertex-deleted subgraph 010103 numerical & computational mathematics 01 natural sciences Distance-regular graph law.invention Combinatorics law Graph power Line graph Discrete Mathematics and Combinatorics Symmetric 2-design 0101 mathematics Complement graph Strongly regular graph Mathematics Discrete mathematics Numerical Analysis Algebra and Number Theory 010102 general mathematics Edge-transitive graph Minimum degree Regular graph Geometry and Topology Main eigenvalue |
| Zdroj: | Linear Algebra and its Applications. 507:462-473 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2016.06.031 |
| Popis: | Let G be a connected non-bipartite graph with exactly three distinct eigenvalues ρ , μ , λ , where ρ > μ > λ . In the case that G has just one non-main eigenvalue, we find necessary and sufficient spectral conditions on a vertex-deleted subgraph of G for G to be the cone over a strongly regular graph. Secondly, we determine the structure of G when just μ is non-main and the minimum degree of G is 1 + μ − λ μ : such a graph is a cone over a strongly regular graph, or a graph derived from a symmetric 2-design, or a graph of one further type. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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