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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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    Official URL: http://www.combinatorics.org/Volume_16/PDF/v16i1r4...


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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:

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