标题： 按共有邻居数对多面体图进行分类 显示英文标题

标题： Classification of polyhedral graphs by numbers of common neighbours

摘要： 我们根据其类型（即每对不同顶点的共同邻居数量的集合）对多面体（平面，$3$-连通图）进行分类。 对于每一个（有限）非负整数集合，我们或者对这类多面体进行全部分类，或者构造出无限多个这类多面体，或者证明不存在这样的多面体。 这个问题与强正则图和Deza图理论、图中的距离以及度序列有关。 在复杂网络和数据科学领域有潜在的应用价值。 显示英文摘要

摘要： We propose a classification of polyhedra (planar, $3$-connected graphs) according to their type i.e., their set of quantities of common neighbours for each pair of distinct vertices. For every (finite) set of non-negative integers, we either classify all the polyhedra of that type, or construct infinitely many polyhedra of that type, or prove that none exist. This problem is related to the theory of strongly regular and Deza graphs, distances in graphs, and degree sequences. There is potential for application to complex networks and data science.