A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph

Citation

Cardoso DM, Cvetkovic D, Rowlinson P & Simic SK (2008) A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph. Linear Algebra and Its Applications, 429 (11-12), pp. 2770-2780. https://doi.org/10.1016/j.laa.2008.05.017

Abstract
We prove that the minimum value of the least eigenvalue of the signless Laplacian of a connected non-bipartite graph with a prescribed number of vertices is attained solely in the unicyclic graph obtained from a triangle by attaching a path at one of its endvertices.

Keywords
Graph theory; Graph spectra; Line graph; Signless Laplacian; Least eigenvalue

Journal
Linear Algebra and Its Applications: Volume 429, Issue 11-12