The 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 G⃞Pn for all connected graphs G on five vertices are also known. In this paper, the crossing numbers of Cartes...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2013-07-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1684 |
| Summary: | 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 G⃞Pn for all connected graphs G on five vertices are also known. In this paper, the crossing numbers of Cartesian products G⃞Pn for graphs G of order six are studied. Let H denote the unique tree of order six with two vertices of degree three. The main contribution is that the crossing number of the Cartesian product H⃞Pn is 2(n − 1). In addition, the crossing numbers of G⃞Pn for fourty graphs G on six vertices are collected |
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| ISSN: | 2083-5892 |