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