Spectral determination of trees with large diameter and small spectral radius

Gao, Xing; Jia, Xuanshi; Wang, Jianfeng; Brunetti, Maurizio

doi:10.22049/cco.2023.28648.1651

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	Spectral determination of trees with large diameter and small spectral radius
Communications in Combinatorics and Optimization
مقاله 1، دوره 9، شماره 4، اسفند 2024، صفحه 607-623 اصل مقاله (529.25 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2023.28648.1651
نویسندگان
Xing Gao¹؛ Xuanshi Jia²؛ Jianfeng Wang¹؛ Maurizio Brunetti^* ³
¹School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China
²Haide School, Ocean University of China, Qingdao 266100, China
³Department of Mathematics and Applications, University of Naples Federico II, Naples, Italy
چکیده
Yuan, Shao and Liu proved that the H-shape tree $H'_n =P_{1,2;n-3}^{1,n-6}$ minimizes the spectral radius among all graphs with order $n\geqslant 9$ and diameter $n-4$. In this paper, we achieve the spectral characterization of all graphs in the set $\mathscr{H}' = \{ H'_n\}_{n\geqslant 8}$. More precisely we show that $H'_n$ is determined by its spectrum if and only if $n \neq 8, 9,12$, and detect all cospectral mates of $H'_8$, $H'_9$ and $H'_{12}$. Divisibility between characteristic polynomials of graphs turns out to be an important tool to reach our goals.
کلیدواژه‌ها
Adjacency spectrum؛ Spectral characterization؛ DS-graph؛ Matchings؛ Spectral radius

مراجع
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Spectral determination of trees with large diameter and small spectral radius