On the Spectrum of Threshold Graphs. (11th December 2011)

• Record Type: Journal Article
• Authors: Sciriha Sciriha, Irene Irene; Farrugia Farrugia, Stephanie Stephanie
• Other Names: Ergun Ergun F. F. Academic Editor.; Feinsilver Feinsilver P. P. Academic Editor.; Hou Hou Y. Y. Academic Editor.; Song Song S. Y. S. Y. Academic Editor.; Trinajstić Trinajstić N. I. N. I. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2011(2011)
• Publication Date: 2011-12-11
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.5402/2011/108509
• Languages: English
• ISSNs: 2090-7788

Abstract

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.