A spectral condition for odd cycles in non-bipartite graphs
| العنوان: | A spectral condition for odd cycles in non-bipartite graphs |
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| المؤلفون: | Huiqiu Lin, Hangtian Guo |
| المصدر: | Linear Algebra and its Applications. 631:83-93 |
| بيانات النشر: | Elsevier BV, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Combinatorics, Numerical Analysis, Algebra and Number Theory, Spectral radius, Bipartite graph, Discrete Mathematics and Combinatorics, Geometry and Topology, Adjacency matrix, Graph, Eigenvalues and eigenvectors, Mathematics |
| الوصف: | Let A ( G ) be the adjacency matrix of a graph G and ρ ( G ) be its spectral radius. Given a graph H and a family F of graphs, let e x s p ( n , H ; F ) = max { ρ ( G ) | | V ( G ) | = n , H ⊆ G , G does not contain any graph of F } . Let S 2 k − 1 ( K s , t ) be the graph obtained by replacing an edge of K s , t with a copy of P 2 k + 1 , where k ≥ 2 . In this paper, we show that e x s p ( n , C 2 k + 3 ; { C 3 , C 5 , … , C 2 k + 1 } ) = ρ ( S 2 k − 1 ( K ⌈ n − 2 k + 1 2 ⌉ , ⌊ n − 2 k + 1 2 ⌋ ) ) and the unique extremal graph is S 2 k − 1 ( K ⌈ n − 2 k + 1 2 ⌉ , ⌊ n − 2 k + 1 2 ⌋ ) , which solves a question proposed in [Eigenvalues and triangles in graphs, Comb. Probab. Comput. 30 (2021) 258–270]. |
| تدمد: | 0024-3795 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_________::69a993e711b8c400ae221163f6dce3d3Test https://doi.org/10.1016/j.laa.2021.08.020Test |
| حقوق: | CLOSED |
| رقم الانضمام: | edsair.doi...........69a993e711b8c400ae221163f6dce3d3 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 00243795 |
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