Published in
Elsevier, Linear Algebra and its Applications, 10(435), p. 2375-2381, 2011
DOI: 10.1016/j.laa.2010.10.020
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On eigenvalue multiplicity and the girth of a graph
Journal article published in 2011 by
Peter Rowlinson
This paper is made freely available by the publisher.
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Abstract
Suppose that G is a connected graph of order n and girth gn. 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.