On the Spectrum of Threshold Graphs

Abstract EN

The antiregular connected graph on r vertices is defined as the connected graph whose vertex degrees take the values of r−1 distinct positive integers.

We explore the spectrum of its adjacency matrix and show common properties with those of connected threshold graphs, having an equitable partition with a minimal number r of parts.

Structural and combinatorial properties can be deduced for related classes of graphs and in particular for the minimal configurations in the class of singular graphs.