联图S5∨Cn的交叉数

On the Crossing Numbers of Join of S_5 ∨ C_n

两个图G和H的联图,记作G∨H,是指将G中每个点与H中的每个点连边得到的图.本文证明了星图S_5与圈C_n的联图S_5∨C_n的交叉数为Z(6,n)+4[n/2]+3(n≥3),其中Z(m,n)=[m/2][(m-1)/2][n/2][(n-1)/2],m,n为非负整数.

By connecting each vertex of a graph G to each vertex of a graph H, join graph, denoted by G V H, is obtained. In this paper, we have proved that the crossing number of S5 V Cn is Z（6, n） ＋ 4[n/2] ＋ 3, where Z（m, n） =[m/2,[m-1/2][n/2][n-1/2]and both m and n are nonnegative integers.