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Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 4 / 16H / iv

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2017 ii Paper 4 16H
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iv
If a regular graph has c>1 connected components, the indicator vector of each component is a Δ-eigenvector. They are linearly independent, and the Laplacian argument shows that every such eigenvector is constant on each component. Therefore its multiplicity is exactly c, in particular greater than one.

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