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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...
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 |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/1642 |
| 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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