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arXiv · 2603.09614

Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs

Guoce Xin·Yueming Zhong·Yangbiao Zhou
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Abstract

Stanley's theorem establishes that for any finite graph $G$, the number $h_G(s)$ of magic labelings with magic sum $s$ can be expressed as a sum of two polynomials in $s$. However, determining the precise form of $h_G(s)$ is generally challenging. This paper aims to compute $h_G(s)$ and its generating function for pseudo-line graphs and pseudo-cycle graphs, thereby extending the earlier work of Bóna et al.\cite{Bona-1,Bona}.

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Guoce Xin, Yueming Zhong, Yangbiao Zhou. 2026-03-10. Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs. https://arxiv.org/abs/2603.09614

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