最大圈长为8的测地块的构造及其性质

The constructions and properties of geodesic block with C_8 as its maximal cycle

测地图的研究主要集中在对测地块的构造以及最大圈长为偶数的测地图的结构方面 .本文给出了测地块中 8-圈及其割线的结构形式 ,并得出一个图是直径为 3测地块的一个充分必要条件 ,从而解决了测地图研究中的两个公开问题 .

The exposition of geodesic graph mainly focusses on the construction of the geodesic block and the structure of the geodesic graph with the maximal even cycles. In this paper we characterized the constructions for the geodesic block with C_8 as its maximal cycle, and we got a sufficient and necessary condition for a graph to be geodesic with diameter 3. Therefore we have solved two open problems in the research field of geodesic graph.