Discussiones
Mathematicae Graph Theory 19(1) (1999) 59-69
DOI: https://doi.org/10.7151/dmgt.1085
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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Received 9 June 1998
Revised 21 November 1998
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