# The crossing numbers of join products of paths with graphs of order four

• Volume: 31, Issue: 2, page 321-331
• ISSN: 2083-5892

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## Abstract

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Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numbers of graphs obtained as join product of two graphs. In the paper, the exact values of crossing numbers for join of paths with all graphs of order four, as well as for join of all graphs of order four with n isolated vertices are given.

## How to cite

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Marián Klešč, and Stefan Schrötter. "The crossing numbers of join products of paths with graphs of order four." Discussiones Mathematicae Graph Theory 31.2 (2011): 321-331. <http://eudml.org/doc/271023>.

@article{MariánKlešč2011,
abstract = {Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numbers of graphs obtained as join product of two graphs. In the paper, the exact values of crossing numbers for join of paths with all graphs of order four, as well as for join of all graphs of order four with n isolated vertices are given.},
author = {Marián Klešč, Stefan Schrötter},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph; drawing; path; crossing number; join product; joint product},
language = {eng},
number = {2},
pages = {321-331},
title = {The crossing numbers of join products of paths with graphs of order four},
url = {http://eudml.org/doc/271023},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Marián Klešč
AU - Stefan Schrötter
TI - The crossing numbers of join products of paths with graphs of order four
JO - Discussiones Mathematicae Graph Theory
PY - 2011
VL - 31
IS - 2
SP - 321
EP - 331
AB - Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numbers of graphs obtained as join product of two graphs. In the paper, the exact values of crossing numbers for join of paths with all graphs of order four, as well as for join of all graphs of order four with n isolated vertices are given.
LA - eng
KW - graph; drawing; path; crossing number; join product; joint product
UR - http://eudml.org/doc/271023
ER -

## References

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6. [6] F. Harary, P.C. Kainen and A.J. Schwenk, Toroidal graphs with arbitrarily high crossing numbers, Nanta Math. 6 (1973) 58-67. Zbl0285.05104
7. [7] S. Jendrol' and M. Scerbová, On the crossing numbers of Sₘ ×Pₙ and Sₘ ×Cₙ, Casopis pro pestování matematiky 107 (1982) 225-230.
8. [8] M. Klešč, The crossing numbers of Cartesian products of paths with 5-vertex graphs, Discrete Math. 233 (2001) 353-359, doi: 10.1016/S0012-365X(00)00251-X. Zbl0983.05027
9. [9] M. Klešč, The join of graphs and crossing numbers, Electronic Notes in Discrete Math. 28 (2007) 349-355, doi: 10.1016/j.endm.2007.01.049. Zbl1291.05108
10. [10] D.J. Kleitman, The crossing number of ${K}_{5,n}$, J. Combin. Theory (B) 9 (1971) 315-323. Zbl0205.54401
11. [11] V.R. Kulli and M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97. Zbl0982.05084
12. [12] K. Zarankiewicz, On a problem of P. Turán concerning graphs, Fund. Math. 41 (1954) 137-145. Zbl0055.41605

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