12 research outputs found
The crossing number of locally twisted cubes
The {\it crossing number} of a graph is the minimum number of pairwise
intersections of edges in a drawing of . 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 -dimensional hypercube proposed by Erd\H{o}s and Guy, we give upper and
lower bounds of the crossing number of locally twisted cube, which is one of
variants of hypercube.Comment: 17 pages, 12 figure
On the Crossing Number of the Cartesian Product of a Sunlet Graph and a Star Graph
The exact crossing number is only known for a small number of families of
graphs. Many of the families for which crossing numbers have been determined
correspond to cartesian products of two graphs. Here, the cartesian product of
the Sunlet graph, denoted , and the Star graph, denoted
, is considered for the first time. It is proved that the crossing
number of is , and the crossing number of
is . An upper bound for the crossing number of
is also given
The Crossing Number of Two Cartesian Products
There are several known exact results on the crossing number of Cartesian
products of paths, cycles, and complete graphs. In this paper, we find the crossing numbers of Cartesian products of Pn with two special 6-vertex graphs
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
International Journal of Mathematical Combinatorics, Vol.1
The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences