Article ID Journal Published Year Pages File Type
4602347 Linear Algebra and its Applications 2008 12 Pages PDF
Abstract

We continue our investigation of graphs G 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, P. Rowlinson, S.K. Simić, Graphs for which the least eigenvalue is minimal, I, Linear Algebra Appl. (2008), doi: 10.1016/j.laa.2008.02.032]; here we distinguish the cases of bipartite and non-bipartite graphs in terms of size.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory