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Citation

Rowlinson P (2014) Eigenvalue multiplicity in cubic graphs. Linear Algebra and Its Applications, 444, pp. 211-218. https://doi.org/10.1016/j.laa.2013.11.036

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=2K3?.

Keywords
Cubic graph; Eigenvalue; Star complement

Journal
Linear Algebra and Its Applications: Volume 444

• Cubic3A.pdf