Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914382640840704 |
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| author | Xin, Guoce Zhong, Yueming Zhou, Yangbiao |
| author_facet | Xin, Guoce Zhong, Yueming Zhou, Yangbiao |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs Xin, Guoce Zhong, Yueming Zhou, Yangbiao Combinatorics Primary 05A19, Secondary 11D04, 05C78 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}. |
| title | Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs |
| topic | Combinatorics Primary 05A19, Secondary 11D04, 05C78 |
| url | https://arxiv.org/abs/2603.09614 |