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MiS Preprint

Petals and Books: The largest Laplacian spectral gap from 1

Jürgen Jost, Raffaella Mulas and Dong Zhang


We prove that, for any connected graph on $N\geq 3$ 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).

Oct 19, 2021
Oct 19, 2021
Spectral graph theory, normalized Laplacian, Spectral gaps, Eigenvalue 1

Related publications

2023 Journal Open Access
Jürgen Jost, Raffaella Mulas and Dong Zhang

Petals and books : the largest Laplacian spectral gap from 1

In: Journal of graph theory, 104 (2023) 4, pp. 727-756