English

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

Combinatorics 2024-09-04 v1

Abstract

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

Keywords

Cite

@article{arxiv.2409.00516,
  title  = {A note on an infinite family of graphs with all different integral Laplacian eigenvalues},
  author = {C. Dalfó and M. A. Fiol},
  journal= {arXiv preprint arXiv:2409.00516},
  year   = {2024}
}