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arXiv · 2307.07275

Integral Laplacian graphs with a unique double Laplacian eigenvalue, II

Abdul Hameed·Mikhail Tyaglov
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Abstract

The set $S_{\{i,j\}_{n}^{m}}=\{0,1,2,\ldots,m-1,m,m,m+1,\ldots,n-1,n\}\setminus\{i,j\},\quad 0<i<j\leqslant n$, is called Laplacian realizable if there exists a simple connected graph $G$ whose Laplacian spectrum is $S_{\{i,j\}_{n}^{m}}$. In this case, the graph $G$ is said to realize $S_{\{i,j\}_{n}^{m}}$. In this paper, we completely describe graphs realizing the sets $S_{\{i,j\}_{n}^{m}}$ with $m=1,2$ and determine the structure of these graphs.

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Abdul Hameed, Mikhail Tyaglov. 2023-07-14. Integral Laplacian graphs with a unique double Laplacian eigenvalue, II. https://doi.org/10.4134/bkms.b230076

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