On the extreme complexity of certain nearly regular graphs
Combinatorics
2025-02-12 v1
Abstract
The complexity of a graph is the number of its labeled spanning trees. It is demonstrated that the seven known triangle-free strongly regular graphs, such as the Higman-Sims graph, are graphs of maximal complexity among all graphs of the same order and degree; their complements are shown to be of minimal complexity. A generalization to nearly regular graphs with two distinct eigevalues of the Laplacian is presented. Conjectures and applications of these results to biological problems on neuronal activity are described.
Keywords
Cite
@article{arxiv.2502.06886,
title = {On the extreme complexity of certain nearly regular graphs},
author = {Gregory P Constantine and Gregory C Magda},
journal= {arXiv preprint arXiv:2502.06886},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:2501.18019