NUI Maynooth

NUIM ePrints and eTheses Archive

NUIM Library

Near Threshold Graphs

Kirkland, Steve (2009) Near Threshold Graphs. Electronic Journal of Combinatorics, 16 (1). ISSN 1077-8926

[img] Download (200kB)
Official URL: http://www.combinatorics.org/Volume_16/PDF/v16i1r4...

Abstract

A conjecture of Grone and Merris states that for any graph G, its Laplacian spectrum, A(G), is majorized by its conjugate degree sequence, D∗(G). That conjecture prompts an investigation of the relationship between A∗(G) and D∗(G), and Merris has characterized the graphs G for which the multisets A∗(G) and D∗(G) are equal. In this paper, we provide a constructive characterization of the graphs G for which A(G) and D∗(G) share all but two elements.

Item Type: Article
Keywords: Grone and Merris states; Laplacian spectrum; NT graphs; Hamilton Institute.
Subjects: Science & Engineering > Hamilton Institute
Science & Engineering > Mathematics
Item ID: 1642
Depositing User: Hamilton Editor
Date Deposited: 04 Nov 2009 17:03
Journal or Publication Title: Electronic Journal of Combinatorics
Publisher: American Mathematical Society
Refereed: Yes
URI:

Repository Staff Only(login required)

View Item Item control page

Document Downloads

More statistics for this item...