On The Crossing Number Of Join Of Some Graphs

In recent years, more and more scholars began to do researches on the crossing numbers of join of some low order graphs with path and cycle. Klesc has solved the crossing numbers of join of all the4-vertex graphs with path and cycle, including unconnected graphs. Others got the crossing numbers of the join products of some5-vertex graphs with path and cycle successively. In2010, Klesc verified the crossing numbers of join of a special graph on six vertices with path and cycle,enriched the results of the join product of two graphs on the crossing number. In this paper, we study the join of graphs by further on the basis of conclusions we already have. We solve the crossing number of join of K2,4with path and cycle, verify the crossing numbers of join of two special unconnected graphs with nK1, and get four inference. What is more, we obtain a lower bound for the crossing numbers of join of other two special unconnected graphs with nK1.The main conclusions we have get in this paper are as follows.(1)Using the structural characteristics of K2,4, the crossing numbers of join of K2,4with path and cycle are obtained.(2)Verified the crossing numbers of join of a special5-vertex graph with nK1, and got two inferences.(3)Verified the crossing numbers of join of a special6-vertex graph with nK1, and got two inferences.(4)Using the combinatorial counting method, we obtained a lower bound for the crossing numbers of join of other two special unconnected graphs with nK1.