The Crossing Numbers of Join of Path and Cycle with a Special Graph of Order Six

Liping Li1,2, Min Li3, Junliang Cai1
1School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, China
2School of Applied Science, Taiyuan University of Science and Technology, Shanxi, 030024, China
3Department of Mathematics & Computer Sciences, Hubei University of Arts and Science, Xiangyang, 441053, China

Abstract

Only few results concerning crossing numbers of join of some graphs are known. In the paper, for the special graph \(G\) on six vertices, we give the crossing numbers of \(G\vee P_n\) and \(G\vee C_n\), \(P_n\) and \(C_n\) are the path and cycle on \(n\) vertices, respectively.