Graphs for which the least eigenvalue is minimal , I
نویسندگان
چکیده
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. © 2008 Elsevier Inc. All rights reserved. AMS classification: 05C50
منابع مشابه
Graphs for which the least eigenvalue is minimal, II
We continue our investigation of graphsG for which the least eigenvalue λ(G) is minimal among the connected graphs of prescribed order and size. We provide structural details of the bipartite graphs that arise, and study the behaviour of λ(G) as the size increases while the order remains constant. The non-bipartite graphs that arise were investigated in a previous paper [F.K. Bell, D. Cvetković...
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