Graph theory and enumerative combinatorics are two branches of mathematical sciences that have developed astonishingly over the past one hundred years. It is especially important to point out that graph theory employs combinatorial techniques to solve key problems of characterization, construction, enumeration and classification of an enormous set of different families of graphs. This paper describes the construction of two classes of bigeodetic blocks using balanced incomplete block designs (BIBDs). On the other hand, even though graph theory and combinatorics have a close relationship, the opposite problem, that is, considering certain graph constructions when solving problems of combinatorics is not common, but possible. The construction of the second class of bigeodetic blocks described in this paper represents an example of how graph theory could somehow give a clue to the description of a problem of existence in combinatorics. We refer to the problem of existence for biplanes. A connection between the mentioned construction, the Bruck-Ryser-Chowla theorem and the problem of existence for biplanes is considered.

翻译：图论与枚举组合数学是数学科学的两大分支，在过去一百年间取得了惊人的发展。尤其需要指出的是，图论运用组合技术解决了大量不同图族特征刻画、构造、枚举与分类的关键问题。本文描述了利用平衡不完全区组设计（BIBDs）构造两类双测地块的方法。另一方面，尽管图论与组合数学关系密切，但逆向问题——即在解决组合数学问题时考虑特定图论构造——虽然不常见却存在可能性。本文所描述的第二类双测地块构造，展示了图论如何为组合数学中的存在性问题提供解决线索的范例。我们聚焦于双平面的存在性问题，并探讨了上述构造、Bruck-Ryser-Chowla定理与双平面存在性问题之间的关联。