應(yīng)yl7703永利官網(wǎng)張和平教授和高毓平博士邀請，美國佐治亞州立大學(xué)陳冠濤教授將于2023年3月30日作線上學(xué)術(shù)報告。

報告題目：Multiplicity of the second-largest eigenvalue of graphs

報告時間：2023年3月30日19:00

騰訊會議ID：663969747

報告摘要：The multiplicity of the second-largest eigenvalue of the adjacency matrix A(G) of a connected graph G, denoted by m(λ₂,G), is the number of times of the second-largest eigenvalue of A(G) appears. In 2019, Jiang, Tidor, Yao, Zhang and Zhao gave an upper bound on m(λ₂,G) for graphs G with bounded degrees, and applied it to solve a longstanding problem on equiangular lines. We showed that if G is a 3-connected planar graph or 2-connected outerplanar graph, then m(λ₂,G)≤δ(G), where δ(G) is the minimum degree of G. We further prove that if G is a connected planar graph, then m(λ₂,G)≤?(G); if G is a connected outerplanar graph, then m(λ₂,G)≤max{2,?(G)-1}, where ?(G) is the maximum degree of G. Moreover, these two upper bounds for connected planar graphs and outerplanar graphs, respectively, are best possible. We will discuss general techniques and specific methods we used in the proofs of these results.

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報告人簡介

陳冠濤，美國佐治亞州立大學(xué)教授(the Regents’Professor)。主要研究圖的結(jié)構(gòu)問題，如圖的圈和路、圖染色和圖的Ramsey理論。解決了圖論領(lǐng)域10余個著名猜想。在組合與圖論領(lǐng)域重要學(xué)術(shù)期刊發(fā)表論文150余篇。曾擔(dān)任SIAM離散數(shù)學(xué)活動的組織者(2014-2016)，2011年以來任圖論組合權(quán)威期刊《Graphs and Combinatorics》執(zhí)行編委。

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2023年3月29日