整数环上射影直线距离图的最短路问题
The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of Integers
摘要：
考虑整数环上射影直线的距离图$G = G(\mathbb{P}(Z),\triangle)$.利用Klein对欧氏连分数的几何解释，解决了该图的最短路问题。在最短路不唯一的情况下，给出了所有可能的分裂，从而给出了存在唯一最短路的充要条件。
英文摘要：
The distant graph $G = G(\mathbb{P}(Z),\triangle)$ of the projective line over the ring of integers is considered. The shortest path problem in this graph is solved by use of Klein's geometric interpretation of Euclidean continued fractions. In case the minimal path is non-unique, all the possible splitting are described which allows us to give necessary and sufficient conditions for existence of a unique shortest path.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
