|Appears in Collections:||Computing Science and Mathematics Journal Articles|
|Peer Review Status:||Refereed|
|Title:||Graphs for which the least eigenvalue is minimal, I|
|Authors:||Bell, Francis K|
Simic, Slobodan K
Nested split graph
|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.|
|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.|
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