On the normalized spectrum of threshold graphs

Abstract

In this article we investigate normalized adjacency eigenvalues (simply normalized eigenvalues) and normalized adjacency energy of connected threshold graphs. A threshold graph can always be represented as a unique binary string. Certain eigenvalues are obtained directly from its binary representation and the rest of the eigenvalues are evaluated from its normalized equitable partition matrix. Finally, we characterize threshold graphs with at most five distinct eigenvalues.

16 pages, 3 figures, final version will appear in Linear Algebra and its Application

Cited by in corpus (4)

• Spectral characterizations of anti-regular graphs
• The role of the anti-regular graph in the spectral analysis of threshold graphs
• Laplacian Controllability of Threshold Graphs
• The normalized Laplacian and related indexes of graphs with edges blew up by cliques