Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs
Combinatorics
2026-03-11 v1
Abstract
Stanley's theorem establishes that for any finite graph , the number of magic labelings with magic sum can be expressed as a sum of two polynomials in . However, determining the precise form of is generally challenging. This paper aims to compute and its generating function for pseudo-line graphs and pseudo-cycle graphs, thereby extending the earlier work of B\'{o}na et al.\cite{Bona-1,Bona}.
Keywords
Cite
@article{arxiv.2603.09614,
title = {Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs},
author = {Guoce Xin and Yueming Zhong and Yangbiao Zhou},
journal= {arXiv preprint arXiv:2603.09614},
year = {2026}
}