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Near Threshold Graphs

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

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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 & 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

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