The generalized Petersen graph P(n, k) is the graph whose vertex set is U ∪ W, where U = {u_0, u_1, ...,u_(n-1)} W = {v_0, v_1,...,v_(n-1)}; and whose edge set is {u_iu_(i+1), u_iv_i, v_iv_i+k| i = 0,1, ... , n - 1}, where n, k are positive integers, addition is modulo n, and 2 ≤ k ≤n/2 .G.Exoo, F.Harary and J.Kabell have determined the crossing number of P(n, 2); Richter and Salazar have determined the crossing number of the generalized Petersen graph P(n, 3). In this paper, the crossing number of the generalized Petersen graph P(3k, k) (k ≥ 4) is studied, and it is proved that cr(P(3k, k)) = k (k ≥4).
展开▼
机译：广义Petersen图P（n，k）是其顶点集为U∪W的图，其中U = {u_0，u_1，...，u_（n-1）} W = {v_0，v_1，... ，v_（n-1）};并且其边集为{u_iu_（i + 1），u_iv_i，v_iv_i + k | i = 0,1，...，n-1}，其中n，k是正整数，加法是n模，并且2≤k≤n/2。G.Exoo，F.Harary和J.Kabell已确定P（n，2）的交叉数; Richter和Salazar已确定了广义Petersen图P（n，3）的交叉数。本文研究了广义Petersen图P（3k，k）（k≥4）的穿越数，并证明cr（P（3k，k））= k（k≥4）。
展开▼
