$K_{2,3}$的剖分图与$P_n, C_n$的联图交叉数

The Crossing Numbers of Join of a Subdivision of $K_{2,3}$ with $P_{n}$ and $C_{n}$

中文关键词:  交叉数  联图  路图  圈图

英文关键词:crossing number  join graph  path  cycle

中文摘要:

      在完全图$K_{2,3}$的任意一边增加一个新的顶点, 则得到$K_{2,3}$的一个剖分图(六阶图). 本文研究得到了这个特殊六阶图与$n$个孤立点$nK_1$, 路$P_n$, 圈$C_n$的联图交叉数.

英文摘要:

      Adding a new vertex to any edge of the complete bipartite graph $K_{2,3}$ gives a subdivision of $K_{2,3}$ (6-vertices graph). In the paper, we get the crossing numbers of the join graph of the specific 6-vertices graph $H$ with $n$ isolated vertices as well as with the path $P_{n}$ on $n$ vertices and with the cycle $C_{n}$.