六阶图C_6+3K_2与P_n, C_n的联图交叉数

Abstract

Abstract:

Let P_n be the path on n vertices, C_n be the cycle with n edges, C_6+3K_2 be the graph which is obtained from the cycle C_6 by adding three adjacent edges. In the paper, for special graph C_6+3K_2, we give the crossing numbers of its join product with the path P_n as well as the cycle C_n are Z(6,n)+3\lfloor \frac{n}{2} \rfloor+2 and Z(6,n)+3\lfloor \frac{n}{2} \rfloor+4. Our proof depends on Kleitman's results for the complete bipartite graph cr(K_{6,n})=Z(6,n).

Key words: crossing number, join product, path, cycle

SU Zhenhua. The crossing number of the join product of C_6+3K_2 with P_n and C_n[J]. Operations Research Transactions.

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The crossing number of the join product of C_6+3K_2 with P_n and C_n

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