The crossing numbers of certain Cartesian products
نویسنده
چکیده
In this article we determine the crossing numbers of the Cartesian products of given three graphs on five vertices with paths.
منابع مشابه
On the crossing numbers of Cartesian products with trees
Zip product was recently used in a note establishing the crossing number of the Cartesian product K1,n2Pm. In this paper, we further investigate the relations of this graph operation with the crossing numbers of graphs. First, we use a refining of the embedding method bound for crossing numbers to weaken the connectivity condition under which the crossing number is additive for the zip product....
متن کاملThe crossing numbers of products of path with graphs of order six
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path Pn of length n, the crossing numbers of Cartesian products G Pn for all connected graphs G on five vertices are also known. In this paper, the crossing numbers of Cartesian products G Pn for graphs G of order six are studied. Let H denote the unique tree of order si...
متن کاملOn the crossing numbers of Cartesian products of stars and graphs of order six
The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. According to their special structure, the class of Cartesian products of two graphs is one of few graph classes for which some exact values of crossing numbers were obtained. The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are ...
متن کاملSome crossing numbers of products of cycles
The exact values of crossing numbers of the Cartesian products of four special graphs of order five with cycles are given and, in addition, all known crossing numbers of Cartesian products of cycles with connected graphs on five vertices are summarized.
متن کاملOn the crossing numbers of Cartesian products of paths with special graphs
There are known exact results of the crossing numbers of the Cartesian product of all graphs of order at most four with paths, cycles and stars. Moreover, for the path Pn of length n, the crossing numbers of Cartesian products G Pn for all connected graphs G on five vertices and for forty graphs G on six vertices are known. In this paper, we extend these results by determining the crossing numb...
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عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 15 شماره
صفحات -
تاریخ انتشار 1995