Speaker：Ziqing Xiang (Southern University of Science and Technology)

Time：2025-7-7 10:30

Location：Conference Room S107 at Experiment Building at Haiyun Campus

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. 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.