2 research outputs found
An upper bound for the crossing number of augmented cubes
A {\it good drawing} of a graph 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 is the minimum number of pairwise intersections of edges in a good
drawing of in the plane. The {\it -dimensional augmented cube} ,
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 less than
.Comment: 39 page
The Conditional Strong Matching Preclusion of Augmented Cubes
The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube , which is a variation of the hypercube that possesses favorable properties