标题： $k$-边测地图 显示英文标题

标题： $k$-edge geodetic graphs

摘要： 一个图$G$是$k$-边测地图，如果$G$的每条边都至少位于一条长度为$k$的测地线上。我们研究了$k$-边测地图的一些基本性质。 我们研究了完全二分图$K_{m,n}$的$k$边测地性，并提供了可以覆盖$K_{m,n}$的最大固定阶路径的最小数量。 我们还研究了树和笛卡尔乘积、强乘积、科罗纳乘积等乘积图的$k$边测地性，并提供了可以覆盖图的最大固定阶路径的最小数量的界限。 显示英文摘要

摘要： A graph $G$ is $k$-edge geodetic graph if every edge of $G$ lies in at least one geodesic of length $k$. We studied some basic properties of $k$-edge geodetic graphs. We investigated the $k$ edge-geodeticity of complete bipartite graph $K_{m,n}$ and provide the minimum number of largest fixed order path that can cover $K_{m,n}$. We also studied the $k$-edge geodeticity of tree and the product graphs like Cartesian product, Strong product, Corona product, and provide the bounds for the minimum number of the largest fixed order path that can cover the graph.