Brualdi–Hoffman–Turán problem of the gem

A graph is said to be F-free if it does not contain F as a subgraph. Brualdi–Hoffman– Turán type problem seeks to determine the maximum spectral radius of an F-free graph with given size. The gem consists of a path on 4 vertices, along with an additional vertex that is adjacent to every vertex of th...

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Bibliographic Details
Published inDiscrete mathematics Vol. 348; no. 10; p. 114528
Main Authors Chen, Fan, Yuan, Xiying
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2025
Subjects
Brualdi–Hoffman–Turán type problem
Gem
Spectral radius
Spectral radius
Brualdi–Hoffman–Turán type problem
Gem
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Summary:A graph is said to be F-free if it does not contain F as a subgraph. Brualdi–Hoffman– Turán type problem seeks to determine the maximum spectral radius of an F-free graph with given size. The gem consists of a path on 4 vertices, along with an additional vertex that is adjacent to every vertex of the path. Concerning Brualdi–Hoffman–Turán type problem of the gem, when the size is odd, Zhang and Wang (2024) [20] and Yu et al. (2025) [18] solved it. In this paper, we completely solve the Brualdi–Hoffman–Turán type problem of the gem.
ISSN:0012-365X
DOI:10.1016/j.disc.2025.114528