ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2017-2018): c. 84%
Mathematicae Graph Theory 19(1) (1999) 59-69DOI: 10.7151/dmgt.1085
Department of Mathematics
Faculty of Electrical Engineering and Informatics
Technical University, 042 00 Košice, Slovak Republic
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.
Received 9 June 1998
Revised 21 November 1998