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The unique spectral extremal graph for intersecting cliques or intersecting odd cycles.
- Source :
-
Linear Algebra & its Applications . May2024, Vol. 689, p176-195. 20p. - Publication Year :
- 2024
-
Abstract
- The (k , r) -fan, denoted by F k , r , is the graph consisting of k copies of the complete graph K r which intersect in a single vertex. Desai et al. [7] proved that E X s p (n , F k , r) ⊆ E X (n , F k , r) for sufficiently large n , where E X s p (n , F k , r) and E X (n , F k , r) are the sets of n -vertex F k , r -free graphs with maximum spectral radius and maximum size, respectively. In this paper, the set E X s p (n , F k , r) is uniquely determined for n large enough. Let H s , t 1 , ... , t k be the graph consisting of s triangles and k odd cycles of lengths t 1 , ... , t k ≥ 5 intersecting in exactly one common vertex, denoted by H s , k for short. Li and Peng [12] showed that E X s p (n , H s , k) ⊆ E X (n , H s , k) for n large enough. In this paper, the set E X s p (n , H s , k) is uniquely characterized for sufficiently large n. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMPLETE graphs
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 689
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 176270210
- Full Text :
- https://doi.org/10.1016/j.laa.2024.02.025