English

On Counting Constructions and Isomorphism Classes of $I$-Graphs

Combinatorics 2024-12-30 v1

Abstract

We prove a collection of asymptotic density results for several interesting classes of the II-graphs. Specifically, we quantify precisely the proportion of II-graphs that are generalised Petersen graphs as well as those that are connected. Our results rely on the estimation of sums over tuples satisfying various coprimality conditions along with other techniques from analytic number theory.

Keywords

Cite

@article{arxiv.2412.19618,
  title  = {On Counting Constructions and Isomorphism Classes of $I$-Graphs},
  author = {Harrison Bohl and Adrian W. Dudek},
  journal= {arXiv preprint arXiv:2412.19618},
  year   = {2024}
}

Comments

18 pages, comments quite welcome!

R2 v1 2026-06-28T20:49:51.111Z