報告人：張建斌副教授（華南師范大學）

報告時間：2024年4月15日上午9:20

報告地點：數(shù)學系715教室

報告摘要：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) 168–177].

Let be the set of ??-vertex connected graphs with odd diameter d, where each graph ?? in   has a diametrical path whose center edge is a cut edge of ??. For any graph ?? 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

報告人簡介：張建斌,華南師范大學副教授,從事化學圖論和代數(shù)圖論的研究,，在《 Linear Algebra Appl.》《Discrete Math.》《Discrete Applied Math.》《J. Math. Chem.》《MATCH Commun. Math. Comput.Chem.》等SCI雜志上發(fā)表論文三十多篇,。

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