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http://hdl.handle.net/1893/18445| Appears in Collections: | Computing Science and Mathematics Journal Articles |
| Peer Review Status: | Refereed |
| Title: | Graphs for which the least eigenvalue is minimal, I |
| Author(s): | Bell, Francis K Cvetkovic, Dragos Rowlinson, Peter Simic, Slobodan K |
| Contact Email: | peter.rowlinson@stir.ac.uk |
| Keywords: | Graph spectrum Largest eigenvalue Least eigenvalue Nested split graph |
| Issue Date: | Jul-2008 |
| Date Deposited: | 28-Jan-2014 |
| Citation: | Bell FK, Cvetkovic D, Rowlinson P & Simic SK (2008) Graphs for which the least eigenvalue is minimal, I. Linear Algebra and Its Applications, 429 (1), pp. 234-241. https://doi.org/10.1016/j.laa.2008.02.032 |
| Abstract: | Let G be a connected graph whose least eigenvalue λ(G) is minimal among the connected graphs of prescribed order and size. We show first that either G is complete or λ(G) is a simple eigenvalue. In the latter case, the sign pattern of a corresponding eigenvector determines a partition of the vertex set, and we study the structure of G in terms of this partition. We find that G is either bipartite or the join of two graphs of a simple form. |
| DOI Link: | 10.1016/j.laa.2008.02.032 |
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|---|---|---|---|---|
| graphs for which.pdf | Fulltext - Published Version | 130.34 kB | Adobe PDF | View/Open |
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