The Crossing Numbers of $K_{5}+P_{n}$
Received:October 27, 2017  Revised:May 17, 2018
Key Word: crossing number   join product   complete graph   path  
Fund ProjectL:Supported by the Natural Science Foundation of Hunan Province (Grant No.2017JJ3251).
Author NameAffiliation
Zhenhua SU Department of Mathematics, Huaihua University, Hunan 418008, P. R. China 
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      A join graph denoted by $G+H$, is illustrated by connecting each vertex of graph $G$ to each vertex of graph $H$. In this paper, we prove the crossing number of join product of $K_{5}+P_{n}$ is $Z(5,n)+2n+\lfloor \frac{n}{2} \rfloor+4$ for $n\geq 2$.
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