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Elsevier, Linear Algebra and its Applications, (444), p. 211-218, 2014

DOI: 10.1016/j.laa.2013.11.036

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Eigenvalue multiplicity in cubic graphs

Journal article published in 2014 by Peter Rowlinson
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Let G be a connected cubic graph of order n with μ as an eigenvalue of multiplicity k. We show that (i) if μ∉{-1,0} then k≤12n, with equality if and only if μ=1 and G is the Petersen graph; (ii) if μ=-1 then k≤12n+1, with equality if and only if G=K4; (iii) if μ= then k≤12n+1, with equality if and only if G=2K 3¯.