Given a graph $G$, a geodesic packing in $G$ is a set of vertex-disjoint maximal geodesics, and the geodesic packing number of $G$, ${\gpack}(G)$, is the maximum cardinality of a geodesic packing in $G$. It is proved that the decision version of the geodesic packing number is NP-complete. We also consider the geodesic transversal number, ${\gt}(G)$, which is the minimum cardinality of a set of vertices that hit all maximal geodesics in $G$. While $\gt(G)\ge \gpack(G)$ in every graph $G$, the quotient ${\rm gt}(G)/{\rm gpack}(G)$ is investigated. By using the rook's graph, it is proved that there does not exist a constant $C < 3$ such that $\frac{{\rm gt}(G)}{{\rm gpack}(G)}\le C$ would hold for all graphs $G$. If $T$ is a tree, then it is proved that ${\rm gpack}(T) = {\rm gt}(T)$, and a linear algorithm for determining ${\rm gpack}(T)$ is derived. The geodesic packing number is also determined for the strong product of paths.

翻译：给定图$G$，$G$中的测地线打包是一组顶点不交的极大测地线，而$G$的测地线打包数${\gpack}(G)$是$G$中测地线打包的最大基数。本文证明了测地线打包数的判定问题是NP完全的。同时，我们考虑测地线横贯数${\gt}(G)$，即击中$G$中所有极大测地线所需顶点集的最小基数。虽然在每个图$G$中$\gt(G)\ge \gpack(G)$成立，但本文研究了商${\rm gt}(G)/{\rm gpack}(G)$的性质。通过使用车图，证明了不存在常数$C < 3$使得对所有图$G$都有$\frac{{\rm gt}(G)}{{\rm gpack}(G)}\le C$成立。若$T$为树，则证明了${\rm gpack}(T) = {\rm gt}(T)$，并推导出确定${\rm gpack}(T)$的线性算法。此外，还确定了路径的强积图的测地线打包数。