arXiv subjects

Wenping Zheng

Publications and source records attributed to Wenping Zheng.

3 recordsLinked to original sources

arXiv2012

An upper bound for the crossing number of augmented cubes

A {\it good drawing} of a graph $G$ is a drawing where the edges are non-self-intersecting and each two edges have at most one point in common, which is either a common end vertex or a crossing. The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a good drawing of $G$ in the plane. The {\it $n$-dimensional augmented cube} $AQ_n$, proposed by S.A. Choudum and V. Sunitha, is an important interconnection network with good topological properties and applications. In this paper, we obtain an upper bound on the crossing number of $AQ_n$ less than $26/324^{n}-(2n^2+7/2n-6)2^{n-2}$.

math.CO↗

arXiv2011

The crossing number of locally twisted cubes

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. Motivated by the recent work [Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper bound on the crossing number of the hypercube. J. Graph Theory {\bf 59}, 145--161 (2008)] which solves the upper bound conjecture on the crossing number of $n$-dimensional hypercube proposed by Erdős and Guy, we give upper and lower bounds of the crossing number of locally twisted cube, which is one of variants of hypercube.

math.CO↗

arXiv2011

The crossing number of folded hypercubes

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. The {\it $n$-dimensional folded hypercube} $FQ_n$ is a graph obtained from $n$-dimensional hypercube by adding all complementary edges. In this paper, we obtain upper and lower bounds of the crossing number of $FQ_n$.

math.CO↗