Speaker: 向子卿副教授，南方科技大学

Inviter: 陈绍示老师

Title: Natural graph spectrum

Language: Chinese

Time & Venue: 2025.06.23 10:00-11:00 思源楼 525

Abstract: We call a graph matrix natural if it can be obtained from the adjacency matrix via a fixed sequence of linear combination, matrix multiplication and Hadamard multiplication. We fix the number of vertices. Typical examples of natural graph matrices are adjacency matrix, adjacency matrix of the complement graph, Laplacian matrix, distance matrix. In this talk, we demonstrate the existence of a natural graph matrix whose spectrum determines the structures of almost all graphs, which answers an open problem by van Dam and Haemers in 2003.