循环图C(9,2)与路P_n的笛卡儿积的交叉数

The Crossing Number of Cartesian Product of Circulant Graph C(9,2) with Path P_n

C(m,2)表示由圈C_m(v_1v_2…v_mv_1)增加边v_iv_(i+2)(i=1,…,m,i+2(mod m))所得的循环图.C(m,2)的一点悬挂(两点悬挂)是增加—个顶点x(两个顶点x,y)和边xv(边xv,yv)的图,其中v∈V(C(m,2)).我们证明了9阶循环图C(9,2)与路P_n的笛卡儿积的交叉数是10n;C(2m-1,2)的一点悬挂和两点悬挂的交叉数分别是m,2m.

C（m, 2） is a circulant graph obtained from Cm（v1v2…vmvq） by adding edges vivi＋2 （i = 1, 2,…, m, i ＋ 2 （mod m））. A single（double） suspension of C（m, 2） is the graph which obtained from C（m, 2） by adding one vertex x （two vertices x and y） and the edges xv （the edges xv, yv） and each v ∈ V（G）. In this paper, we have proved that the crossing number of one and two suspensions of C（2m - 1, 2） are m, 2m,respectively. And we extend the earlier results to the Cartesian products of C（m, 2） × Pn, showing that the crossing number of cartesian product of Pn with circulant graph C（9, 2） is 10n.