If $f:\tilde{\unicode[STIX]{x1D6E4}}\rightarrow \unicode[STIX]{x1D6E4}$ is a covering map between connected graphs, and $H$ is the subgroup of $\unicode[STIX]{x1D70B}_{1}(\unicode[STIX]{x1D6E4},v)$ used to construct the cover, then it is well known that the group of deck transformations of the cover is isomorphic to $N(H)/H$ , where $N(H)$ is the normalizer of $H$ in $\unicode[STIX]{x1D70B}_{1}(\unicode[STIX]{x1D6E4},v)$ . We show that an entirely analogous result holds for immersions between connected graphs, where the subgroup $H$ is replaced by the closed inverse submonoid of the inverse monoid $L(\unicode[STIX]{x1D6E4},v)$ used to construct the immersion. We observe a relationship between group actions on graphs and deck transformations of graph immersions. We also show that a graph immersion $f:\tilde{\unicode[STIX]{x1D6E4}}\rightarrow \unicode[STIX]{x1D6E4}$ may be extended to a cover $g:\tilde{\unicode[STIX]{x1D6E5}}\rightarrow \unicode[STIX]{x1D6E4}$ in such a way that all deck transformations of $f$ are restrictions of deck transformations of $g$ .

中文翻译：

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图形浸入、逆单面体和甲板变换

如果 $f:\波浪号{\unicode[STIX]{x1D6E4}}\rightarrow \unicode[STIX]{x1D6E4}$ 是连通图之间的覆盖图，并且 $H$ 是的子群 $\unicode[STIX]{x1D70B}_{1}(\unicode[STIX]{x1D6E4},v)$ 用于构造覆盖，则众所周知，覆盖的甲板变换群同构于 $N(H)/H$ ， 在哪里 $N(H)$ 是规范化器 $H$ 在 $\unicode[STIX]{x1D70B}_{1}(\unicode[STIX]{x1D6E4},v)$ . 我们证明了一个完全类似的结果适用于连通图之间的沉浸，其中子组 $H$ 被逆幺半群的封闭逆子幺半群代替 $L(\unicode[STIX]{x1D6E4},v)$ 用于构建沉浸感。我们观察了图上的组动作和图沉浸的甲板转换之间的关系。我们还展示了图形沉浸 $f:\波浪号{\unicode[STIX]{x1D6E4}}\rightarrow \unicode[STIX]{x1D6E4}$ 可以扩展到封面 $g:\波浪号{\unicode[STIX]{x1D6E5}}\rightarrow \unicode[STIX]{x1D6E4}$ 以这样一种方式，所有的甲板转换 $f$ 是甲板变换的限制 $g$ .