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 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 eigenvalues of the Laplacian is presented. Conjectures and applications of these results to biological problems on neuronal activity are described.
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This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Constantine, Gregory P. and Magda, Gregory C.
(2026)
"On the extreme complexity of certain nearly regular graphs,"
Theory & Applications of Graphs: Vol. 13:
Iss.
1, Article 1.
DOI: 10.20429/tag.2026.130101
Available at:
https://digitalcommons.georgiasouthern.edu/tag/vol13/iss1/1
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