Computer Engineering and Applications ›› 2014, Vol. 50 ›› Issue (18): 79-84.
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YUE Weijun1, HUANG Yuanqiu1, OUYANG Zhangdong2
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岳为君1,黄元秋1,欧阳章东2
Abstract: By connecting each vertex of a graph [G] to each vertex of a graph [H], a join graph, denoted by [G+H], is obtained. In this paper, based on the crossing number of [W3+Cn] obtained by Klesc M., it gets that the crossing number of [W4+Cn] is [Z(5,n)+n+n2+4(n3)] by reduction to absurdity and elimination method, and gives a conjecture of the crossing number of [Wm+Cn]within the conjecture of Zarankiewicz, [cr(Wm+Cn)=Z(m+1,n)+m2m-12n2+m2+][n2+2,n3], in which [Z(m,n)=m2m-12n2n-12,m,n] is nonnegative integer.
Key words: drawing, crossing number, join graph, [Cn]
摘要: 联图[G+H]表示将[G]中每个点与[H]中的每个点连边得到的图。在Klesc M.给出联图[W3+Cn]的交叉数的基础上,应用反证法和排除法得到了联图[W4+Cn]的交叉数为[Z(5,n)+n+n2+4(n3)],并在Zarankiewicz猜想成立的前提下,根据证明,提出对[Wm+Cn]的交叉数的一个猜想:[cr(Wm+Cn)=Z(m+1,n)+m2m-12n2+m2+n2+2,n3]。其中[Z(m,n)=m2m-12n2n-12,m,n]为非负整数。
关键词: 画法, 交叉数, 联图, 圈
YUE Weijun1, HUANG Yuanqiu1, OUYANG Zhangdong2. On crossing numbers of join of [W4+Cn][J]. Computer Engineering and Applications, 2014, 50(18): 79-84.
岳为君1,黄元秋1,欧阳章东2. 联图[W4+Cn]的交叉数[J]. 计算机工程与应用, 2014, 50(18): 79-84.
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http://cea.ceaj.org/EN/Y2014/V50/I18/79