一个六阶图与星的笛卡儿积交叉数(英文)

Crossing Number of the Cartesian Product of a 6-Vertex Graph with Sn

拓展了目前关于星与低阶图的笛卡儿积交叉数的某些结论,确定了1个特殊6 -阶图与星K1,n的笛卡儿积交叉数为z(6,n)+4n,并给出了1个有在K2,4,n中加入2条边分别联结K2,4,n中2对n+2度点得到的1个特殊图类Hn的交叉数.

There are several known exact results on the crossing numbers of Cartesian products of stars with ＂small＂ graphs. In this paper we extend these results to the cartesian products of a specific 6-vertex with the star K1,n and determine its crossing number is z（6,n）＋4n. In addition we give the crossing number of the graph Hn obtained by adding 2 edges to the graphin K2.4.n such a way that these new edges respectively join a pair of vertices of degree n＋2 of the graph K2.4,n.