区组设计与K-测地图：综述
Block Designs and K-Geodetic Graphs: A Survey
AI总结：
本文综述利用平衡不完全区组设计构造K=1,2,3的K-测地图，围绕刻画、构造、枚举和分类四个核心问题，指出一般分类问题仍开放。
摘要：
K-测地图（K为大写）被定义为图中任意一对不相邻顶点之间至多有K条最短路径的图。当K=1时称为测地图，K=2时称为双测地图，K=3时称为三测地图。K-测地图被有效应用于计算机科学不同领域中若干实际问题的求解，因此其研究具有重要意义。K-测地图的研究围绕四个核心问题，即刻画、构造、枚举和分类。对于K=1,2,3的每一类，K-测地图的一般分类问题仍是开放的。本文是一篇综述，致力于利用平衡不完全区组设计（BIBDs）构造K=1,2,3的K-测地图。为此，我们将区组设计用作由完全预定的参数定义的组合结构，这对于本文所述K-测地图的简便构造至关重要。
英文摘要：
K-geodetic graphs (K capital) are defined as graphs in which each pair of nonadjacent vertices has at most K paths of minimum length between them. A K-geodetic graph is geodetic if K=1, bigeodetic if K=2 and trigeodetic if K=3. K-geodetic graphs are applied effectively to the solution of several practical problems in distinct areas of computer science, hence the importance of their study. Four problems are central to the study of K-geodetic graphs, namely, characterization, construction, enumeration and classification. The problems of finding the general classification of K-geodetic graphs for each of their classes K=1,2,3 are open. The present paper is a survey dedicated to the construction of K-geodetic graphs for K=1,2,3 using balanced incomplete block designs (BIBDs). To this purpose, we use block designs as combinatorial structures defined in terms of completely predetermined parameters, which is essential for the easy construction of the K-geodetic graphs described in this survey.
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。
