115周年校庆“学术Beoplay 中国官网”系列活动之0079:On eccentricity eigenvalues of graphs

来源单位及审核人:编辑:审核发布:数学与信息学院 发布时间:2024-04-12

报告人:张建斌副教授(华南师范大学)

报告时间2024415日上午9:20

报告地点:数学系715教室

报告摘要Given a connected graph G with vertex set V(G), the distance matrix of G is the matrix D(G)=(d_G(u,v))_{u,v\in V(G)}, and the eccentricity matrix of  G is defined as the matrix constructed from the distance matrix of G by keeping for each row and each column  the largest entries  and setting all other entries to be zero, where d_G(u,v) denotes the distance between u and v in G. The eccentricity eigenvalues of G are the eigenvalues of the eccentricity matrix.

  We identify the unique n-vertex tree with diameter 4 and matching number 5 that minimizes the eccentricity spectral radius, and thus resolve a conjecture proposed in [W. Wei, S. Li, L.Zhang, Characterizing the extremal graphs with respect to the eccentricity spectral radius, and beyond, Discrete Math. 345 (2022) 112686].

By interlacing theorem, the least eccentricity eigenvalue of a graph with diameter d is at most -d. We show that this bound is achieved for d\geq 3 if and only if the graph is an antipodal graph with equal diameter and radius, which solves an open problem proposed in [J. Wang, M. Lu, L. Lu, F. Belardo, Spectral properties of the eccentricity matrix of graphs, Discrete Appl. Math. 279 (2020) 168177].

Let be the set of 𝑛-vertex connected graphs with odd diameter d, where each graph 𝐺 in   has a diametrical path whose center edge is a cut edge of 𝐺. For any graph 𝐺 in  . In terms of the energy and spectral radius of the weighted graphs, we determine the graphs with minimum eccentricity energy, minimum and maximum eccentricity spectral radius in  , respectively

报告人简介张建斌,华南师范大学副教授,从事化学图论和代数图论的研究,在《 Linear Algebra Appl.》《Discrete Math.》《Discrete Applied Math.》《J. Math. Chem.》《MATCH Commun. Math. Comput.Chem.》等SCI杂志上发表论文三十多篇。


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