A graph is NIC-planar if it can be drawn in the plane so that there is at most one crossing per edge and two pairs of crossing edges share at most one common end vertex. A (p, 1)-total k-labelling of a graph G is a function f from \(V(G)\cup E(G)\) to the color set \(\{0,1,\ldots ,k\}\) such that \(|f(x)-f(y)|\ge 1\) if \(xy\in E(G)\), \(|f(e_1)-f(e_2)|\ge 1\) if \(e_1\) and \(e_2\) are two adjacent edges in G, and \(|f(x)-f(e)|\ge p\) if a vertex x is incident with the edge e. The minimum k such that G has a (p, 1)-total k-labelling is the (p, 1)-total labelling number of G. In this paper, we prove that the (p, 1)-total labelling number (\(p\ge 2\)) of every NIC-planar graph G is at most \(\Delta (G)+2p-2\) provided that \(\Delta (G)\ge 6p+4.\)

一个图是 NIC 平面的，如果它可以在平面上绘制，使得每条边最多有一个交叉点，并且两对交叉边最多共享一个公共端点顶点。A（p，1） -全ķ的曲线图的-labelling ģ是一个函数˚F从\（V（G）\杯E（G）\）到颜色集合\（\ {0,1，\ ldots，K \}\)使得\(|f(x)-f(y)|\ge 1\)如果\(xy\in E(G)\) , \(|f(e_1)-f(e_2)| \ge 1\)如果\(e_1\)和\(e_2\)是G中的两个相邻边，并且\(|f(x)-f(e)|\ge p\)如果顶点x与边缘电子。最小ķ使得ģ具有（p，1） -全ķ -labelling是（p的，1） -全标号数ģ。在本文中，我们证明每个网卡平面图G的 ( p , 1)-总标记数 ( \(p\ge 2\) )至多为\(\Delta (G)+2p-2\)假设\(\Delta (G)\ge 6p+4.\)