Graphs for which the least eigenvalue is minimal, I

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.

Keywords
Graph spectrum; Largest eigenvalue; Least eigenvalue; Nested split graph

Journal
Linear Algebra and Its Applications: Volume 429, Issue 1