Speaker: Kang Liying, Professor and doctoral supervisor at Shanghai University

Date: March 31, 2023

Time: 9:30-10:30

Location: Tencent Meeting

Sponsor: School of Mathematics, Shandong University

Abstract:

For a simple graph, let and denote set of graphs with the maximum number of edges and the set of graphs with the maximum spectral radius in an -vertex graph without any copy of the graph, respectively. The Turan graph is the complete -partite graph on vertices where its part sizes are as equal as possible. Cioaba, Desai and Tait [The spectral radius of graphs with no odd wheels, European J. Combin., 99 (2022) 103420] posed the following conjecture: Let be any graph such that the graphs in are Turan graphs plus O(1) edges. Then for sufficiently large. In this talk, we consider the graph such that the graphs are obtained from by adding O (1) edges, and prove that if G has the maximum spectral radius among all n-vertex graphs not containing F, then is a member of for large enough. Thus Cioaba, Desai and Tait’s conjecture is completely solved. We also give the spectral extremal graphs for -fan and the unique spectral extremal graph for.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/176971.htm

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