A Laplacian eigenbasis for threshold graphs

Abstract

Let GG be a graph on nn vertices. In this article, we prove that an eigenbasis of the Laplacian matrix of a star graph of order nn is also an eigenbasis of GG if and only if GG is a threshold graph. As an application of this spectral characterization, we show an infinite family of threshold graphs that are weakly Hadamard diagonalizable.

Keywords

• threshold graph
• spectral characterization
• laplacian matrix
• weakly hadamard diagonalizable graph
• 05c50
• 05c35