3 research outputs found

    An upper bound for the crossing number of augmented cubes

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    A {\it good drawing} of a graph GG 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 GG is the minimum number of pairwise intersections of edges in a good drawing of GG in the plane. The {\it nn-dimensional augmented cube} AQnAQ_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 AQnAQ_n less than 26/324n(2n2+7/2n6)2n226/324^{n}-(2n^2+7/2n-6)2^{n-2}.Comment: 39 page
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