# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

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# Discussiones Mathematicae Graph Theory

## THE CROSSING NUMBERS OF PRODUCTS OF A 5-VERTEX GRAPH WITH PATHS AND CYCLES

Marián Klešč

Department of Mathematics
Faculty of Electrical Engineering and Informatics
Technical University, 042 00 Košice, Slovak Republic

e-mail: Klesc@ccsun.tuke.sk

## Abstract

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, and 3n for even n or 3n+1 if n is odd.

Keywords: graph, drawing, crossing number, path, cycle, Cartesian product.

1991 Mathematics Subject Classification: 05C10, 05C38.

## References

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