Linear maps on nonnegative symmetric matrices preserving the independence number

作者：Hu, Yanan; Huang, Zejun^*

来源：Linear Algebra and Its Applications, 2023, 670: 154-167.

DOI：10.1016/j.laa.2023.04.010

• Independence number
• Linear map
• Nonnegative matrix
• Vertex permutation

The independence number of a square matrix A, denoted by alpha(A), is the maximum order of its principal zero submatrices. Given any integer n, let Sn+ be the set of n x n nonnegative symmetric matrices with zero diagonal. We characterize the linear maps on Sn+ preserving the independence number of all matrices in Sn+.