The Crossing Number of Cartesian Product of Circulant Graph C(9,2) with Path Pn
YUAN Zihan1, HUANG Yuanqiu2, LIU Jinwang1
1. College of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, 411201; 2. College of Mathematics and Computer Science, Normal University of Hunan, Changsha, 410081
C(m,2)is a circulant graph obtained from Cm (v1v2…vmv1) by adding edges vivi+2 (i=1,…,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.