English

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 GG, the number hG(s)h_G(s) of magic labelings with magic sum ss can be expressed as a sum of two polynomials in ss. However, determining the precise form of hG(s)h_G(s) is generally challenging. This paper aims to compute hG(s)h_G(s) 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}
}
R2 v1 2026-07-01T11:12:28.908Z