The spectral radius of graphs with no intersecting odd cycles

Let Hs,t1,…,tk be the graph with s triangles and k odd cycles of lengths t1,…,tk≥5 intersecting in exactly one common vertex. Recently, Hou et al. (2018) [27], and Yuan (2018) [42] determined independently the maximum number of edges in an n-vertex graph that does not contain Hs,t1,…,tk as a subgrap...

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Bibliographic Details
Published in:Discrete mathematics 2022-08, Vol.345 (8), p.112907, Article 112907
Main Authors: Li, Yongtao, Peng, Yuejian
Format: Article
Language:English
Subjects:
Extremal graph
Intersecting odd cycles
Spectral radius
Stability method
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Summary:Let Hs,t1,…,tk be the graph with s triangles and k odd cycles of lengths t1,…,tk≥5 intersecting in exactly one common vertex. Recently, Hou et al. (2018) [27], and Yuan (2018) [42] determined independently the maximum number of edges in an n-vertex graph that does not contain Hs,t1,…,tk as a subgraph. In this paper, we determine the graphs of order n that attain the maximum spectral radius among all graphs containing no Hs,t1,…,tk for n large enough.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2022.112907