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The Crossing Numbers of Products of Path with Graphs of Order Six

Marián Klešč;  Jana Petrillová — 2013

Discussiones Mathematicae Graph Theory

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...

On the Crossing Numbers of Cartesian Products of Wheels and Trees

Marián Klešč;  Jana Petrillová;  Matúš Valo — 2017

Discussiones Mathematicae Graph Theory

Bokal developed an innovative method for finding the crossing numbers of Cartesian product of two arbitrarily large graphs. In this article, the crossing number of the join product of stars and cycles are given. Afterwards, using Bokal’s zip product operation, the crossing numbers of the Cartesian products of the wheel Wn and all trees T with maximum degree at most five are established.

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