On the Spectrum of Threshold Graphs. (11th December 2011) - Sciriha Sciriha, Irene Irene; Farrugia Farrugia, Stephanie Stephanie
Abstract : 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.