Brualdi-Hoffman-Tur\'{a}n problem of the gem
Combinatorics
2024-11-14 v1
Abstract
A graph is said to be -free if it does not contain as a subgraph. Brualdi-Hoffman-Tur\'{a}n problem seeks to determine the maximum spectral radius of an -free graph with given size. The gem consists of a path on vertices, along with an additional vertex that is adjacent to every vertex of the path. Concerning Brualdi-Hoffman-Tur\'{a}n 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\'{a}n problem type problem of the gem.
Cite
@article{arxiv.2411.08345,
title = {Brualdi-Hoffman-Tur\'{a}n problem of the gem},
author = {Fan Chen and Xiying Yuan},
journal= {arXiv preprint arXiv:2411.08345},
year = {2024}
}