On eigenvalue multiplicity and the girth of a graph

Citation

Rowlinson P (2011) On eigenvalue multiplicity and the girth of a graph. Linear Algebra and Its Applications, 435 (10), pp. 2375-2381. https://doi.org/10.1016/j.laa.2010.10.020

Abstract
Suppose that G is a connected graph of order n and girth g<n. Let k be the multiplicity of an eigenvalue μ of G. Sharp upper bounds for k are n-g+2 when μ∈{-1,0}, and n-g otherwise. The graphs attaining these bounds are described.

Keywords
Graph; Girth; Eigenvalue; Star complement

Journal
Linear Algebra and Its Applications: Volume 435, Issue 10