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

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 3, page 571-582
- ISSN: 2083-5892

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topMarián Klešč, and Jana Petrillová. "The Crossing Numbers of Products of Path with Graphs of Order Six." Discussiones Mathematicae Graph Theory 33.3 (2013): 571-582. <http://eudml.org/doc/267699>.

@article{MariánKlešč2013,

abstract = {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},

author = {Marián Klešč, Jana Petrillová},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph; drawing; crossing number; Cartesian product; path; tree},

language = {eng},

number = {3},

pages = {571-582},

title = {The Crossing Numbers of Products of Path with Graphs of Order Six},

url = {http://eudml.org/doc/267699},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Marián Klešč

AU - Jana Petrillová

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

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 3

SP - 571

EP - 582

AB - 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

LA - eng

KW - graph; drawing; crossing number; Cartesian product; path; tree

UR - http://eudml.org/doc/267699

ER -

## References

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