Non-planar (3,6)-sparse graphs with various apex properties

In this data set we provide the list of non-planar connected (3-6)sparse graphs with different apex properties. A graph is (3,6)-sparse if if for every subset of n vertices,with at least 3 elements, the number of edges in the subgraph induced by these elements is at most 3n − 6. We call a graph apex if there is a vertex whose deletion gives a planar graph. A graph is critically apex if the deletion of every single vertex yields a planar graph. Similarly (critically) edge-apex graphs are defined with the deletion of edges. Furthermore, k-apex and k-edge-apex graphs are defined by deleting k vertices or edges. The data set provides graphs in Graph6 data format.本数据集收录了具备不同顶点附着属性的非平面连通(3,6)-稀疏图列表。若对于任意顶点数不小于3的顶点子集，其诱导子图的边数至多为3n−6，则称该图为(3,6)-稀疏图。若存在某一顶点，删除该顶点后所得子图为平面图，则称该图为顶点附着图（apex graph）；若删除图中任意单个顶点后所得子图均为平面图，则称该图为临界顶点附着图。类似地，可通过删除边的方式定义边附着图（edge-apex graph）与临界边附着图。进一步地，k-顶点附着图与k-边附着图分别指通过删除k个顶点或k条边后可得到平面图的图。 本数据集采用Graph6数据格式存储图数据。