Elsevier, Linear Algebra and its Applications, 1(429), p. 234-241, 2008
DOI: 10.1016/j.laa.2008.02.032
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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.