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arXiv · 2409.00516

A note on an infinite family of graphs with all different integral Laplacian eigenvalues

C. Dalfó·M. A. Fiol
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Abstract

In this note, we give an infinite family of optimal graphs called $G^+(d,c)$. They are optimal in the sense that they have the maximum possible number of vertices for given a diameter $d$ and the so-called `outer multiset dimension' $c$. We provide their spectra, which have the property that their Laplacian eigenvalues are all different and integral. Finally, we also obtained their eigenvectors.

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C. Dalfó, M. A. Fiol. 2024-08-31. A note on an infinite family of graphs with all different integral Laplacian eigenvalues. https://arxiv.org/abs/2409.00516

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