On the Crossing Numbers of $K_5\times S_n$
Received:June 19, 2006  Revised:March 22, 2007
Key Words: graph   drawing   crossing number   star   Cartesian products.  
Fund Project:the National Natural Science Foundation of China (No.10771062) and New Century Excellent Talents in University.
Author NameAffiliation
L\"{U} Sheng Xiang Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China 
HUANG Yuan Qiu Department of Mathematics, Normal University of Hunan, Hunan 410081, China 
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Abstract:
      By connecting the $5$ vertices of $K_{5}$ to other $n$ vertices, we obtain a special family of graph denoted by $H_{n}$. This paper proves that the crossing number of $H_{n}$ is $Z(5,n)+2n+\lfloor \frac{n}{2} \rfloor+1$, and the crossing number of Cartesian products of $K_{5}$ with star $S_{n}$ is $Z(5,n)+5n+\lfloor \frac{n}{2} \rfloor+1$.
Citation:
DOI:10.3770/j.issn:1000-341X.2008.03.001
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