On the extensional eigenvalues of graphs

作者：

Highlights：

• In this paper, we first propose the extensional eigenvalues of graphs, which generalizes almost all other types of eigenvalues of graphs.

• We present some basic properties of extensional eigenvalues, which also hold for classical eigenvalues.

• Our method provides a consistent method that is valid for all types of graph matrices.

• This paper may open a new door in spectral graph theory.

摘要

•In this paper, we first propose the extensional eigenvalues of graphs, which generalizes almost all other types of eigenvalues of graphs.•We present some basic properties of extensional eigenvalues, which also hold for classical eigenvalues.•Our method provides a consistent method that is valid for all types of graph matrices.•This paper may open a new door in spectral graph theory.

论文关键词：Extensional eigenvalue,Extensional eigenvector,Rayleigh quotient

论文评审过程：Received 22 February 2021, Revised 30 April 2021, Accepted 9 May 2021, Available online 26 May 2021, Version of Record 26 May 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126365