The problem of finding the general classification of geodetic graphs is still open. We believe that one of the obstacles to attain this goal is that geodetic graphs lack a structural description. In other words, their fundamental properties have not yet been established in terms of the description of the complete graphs, paths and cycles contained within them. The absence of this information makes their generation and enumeration (as inherent parts of their general classification) a difficult task. This paper examines the structural qualities of geodetic graphs using their so-called embedded even graphs. To this effect, the necessary and sufficient conditions for eliminating the nongeodecity of each pair of C-opposite vertices in an even cycle C have been formulated, while the bigeodecity of the embedded even graphs of a geodetic graph has been established. In a sense, this allows us to arrive at the conclusion that the basic building blocks of geodetic graphs are precisely this class of bigeodetic ones.

翻译：测地图的一般分类问题至今尚未解决。我们认为实现这一目标的主要障碍在于测地图缺乏结构性描述。换言之，其基本性质尚未通过其内部完全图、路径与环结构的完整描述得以确立。此类信息的缺失使得测地图的生成与枚举（作为其一般分类的内在组成部分）成为一项艰巨任务。本文通过所谓嵌入偶图研究测地图的结构特性。为此，我们建立了偶环C中每对C-对向顶点消除非测地性的充要条件，同时证明了测地图嵌入偶图的双测地性。从某种意义上说，这使我们得出以下结论：测地图的基本构成单元正是这类双测地图。