An Upper Bound for the Crossing Number of Locally Twisted Cubes

Abstract

The crossing number of a graph \(G\) is the minimum number of pairwise intersections of edges in a drawing of \(G\). The \(n\)-dimensional locally twisted cubes \(LTQ_n\), proposed by X.F. Yang, D.J. Evans and G.M. Megson, is an important interconnection network with good topological properties and applications. In this paper, we mainly obtain an upper bound on the crossing number of \(LTQ_n\), no more than \(\frac{265}{6}4^{n-4} – (n^2 + \frac{15+(-1)^{n-1}}{6}2^{n-3}\).