Some crossing numbers of products of cycles
نویسنده
چکیده
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.
منابع مشابه
On 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 ...
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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...
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There are several known exact results on the crossing numbers of Cartesian products of paths, cycles or stars with “small” graphs. Let H be the 5-vertex graph defined from K5 by removing three edges incident with a common vertex. In this paper, we extend the earlier results to the Cartesian products of H ×Pn and H ×Cn, showing that in the general case the corresponding crossing numbers are 3n−1...
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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...
متن کاملMinimum Crossings in Join of Graphs with Paths and Cycles
The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. Only few results concerning crossing numbers of graphs obtained as join product of two graphs are known. There was collected the exact values of crossing numbers for join of all graphs of at most four vertices and of several graphs of order five with paths and cycles. We extend these r...
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عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 25 شماره
صفحات -
تاریخ انتشار 2005