The crossing number of locally twisted cubes [formula omitted

Abstract

The 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 et al., 2008) which solves the upper bound conjecture on the crossing number of n-dimensional hypercube proposed by Erdős and Guy, we consider the crossing number of locally twisted cubes LTQn, which is one of important variation of the hypercube Qn. In this paper, we obtain the upper bound of the crossing number of LTQn as follows. cr(LTQn)≤875124n−4n2−15+(−1)n−1322n.