| The Crossing Numbers of Cartesian Products of Stars with a 5-Vertex Graph |
| Received:July 03, 2007 Revised:May 21, 2008 |
| Key Words:
graph drawing crossing number Cartesian products star.
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| Fund Project:the National Natural Science Foundation of China (No.10771062); the New Century Excellent Tallents in University (No.NCET-07-0276). |
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| Abstract: |
| In this paper, we compute the crossing number of a specific graph $H_{n}$, and then by contraction, we obtain the conclusion that ${\rm cr}(G_{13}\times S_{n})=4\lfloor\frac{n}{2}\rfloor\lfloor\frac{n-1}{2}\rfloor \lfloor\frac{n}{2}\rfloor$. The result fills up the blank of the crossing numbers of Cartesian products of stars with all 5-vertex graphs presented by Mari\'{a}n Kle\v{s}\v{c}. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.04.002 |
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