AI 中文总结
本文证明了所有多联骨牌均为$C_4$-面魔术图，完善了平面图面魔术性质的相关研究结论。
AI 中文摘要
对于嵌入在$\boldsymbol{\text{R}}^2$中的平面图$G=(V,E)$，令$\boldsymbol{\text{F}}(G)$表示$G$的面集合。若存在双射$f:V(G)\to\{1,2,\boldsymbol{\text{...}},|V(G)|\}$，使得对任意满足$F\boldsymbol{\text{≅}}C_n$的面$F\boldsymbol{\text{∈}}\boldsymbol{\text{F}}(G)$，沿$C_n$的所有顶点标号之和为常数$c$，则称$G$为$\boldsymbol{C_n}$-面魔术图。本文证明所有多联骨牌都是$\boldsymbol{C_4}$-面魔术图。
英文摘要
For a planar graph $G = (V, E)$ embedded in $\mathbb{R}^2$, let $\mathcal{F}(G)$ denote the set of faces of $G$. Then $G$ is called a \textit{$C_n$-face-magic} graph if there exists a bijection $f: V(G) \to \{1, 2, \dots, |V(G)|\}$ such that for any $F \in \mathcal{F}(G)$ with $F \cong C_n$, the sum of all the vertex labels along $C_n$ is a constant $c$. In this paper, we prove that all polyominoes are $C_4$-face-magic.
