Brualdi-Hoffman-Tur\'an problem of the gem
Abstract
A graph is said to be F-free if it does not contain F as a subgraph. Brualdi-Hoffman-Tur\'an 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-Tur\'an problem of the gem, when the size is odd, Zhang and Wang [Discrete Math. 347 (2024) 114171] and Yu, Li and Peng [arXiv:2404. 03423] solved it. In this paper, we completely solve the Brualdi-Hoffman-Tur\'an problem type problem of the gem.
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