Abstract
C(n, k) is a graph obtained from n-cycle \(C_n\, (v_1\cdots v_nv_1)\) by adding edges v i v i+k (i = 1, 2,...,n, i + k (mod n)). There are several known results on the crossing numbers of the Cartesian products of C(n, k) (n ≤ 7) with paths, cycles and stars. In this paper we extend these results, and show that the crossing number of the Cartesian product of C(8, 2) with P n is 8n.
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Yuanqiu Huang: Research supported by NSFC (10771062) and New Century Excellent Talents in University (NCET-07-0276).
Jinwang Liu: Research supported by NSFC (10771058) and Hunan NSFC(O6jj20053).
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Yuan, Z., Ling, T., Huang, Y. et al. The Crossing Number of C(8, 2)□P n . Graphs and Combinatorics 24, 597–604 (2008). https://doi.org/10.1007/s00373-008-0800-1
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DOI: https://doi.org/10.1007/s00373-008-0800-1