Petals and Books: The largest Laplacian spectral gap from 1

Jürgen Jost, Raffaella Mulas, and Dong Zhang

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Submission date: 19. Oct. 2021
Bibtex
Keywords and phrases: Spectral graph theory, normalized Laplacian, Spectral gaps, Eigenvalue 1
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We prove that, for any connected graph on N ≥ 3 vertices, the spectral gap from the value 1 with respect to the normalized Laplacian is at most 1∕2. Moreover, we show that equality is achieved if and only if the graph is either a petal graph (for N odd) or a book graph (for N even).