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

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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.
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Science and Engineering > Mathematics and Statistics
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:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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