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Discussiones Mathematicae Graph Theory 31(2) (2011)
321-331
DOI: https://doi.org/10.7151/dmgt.1548
THE CROSSING NUMBERS OF JOIN PRODUCTS OF PATHS WITH GRAPHS OF ORDER FOUR
Marián Klešč and Stefan Schrötter
Department of Mathematics |
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.Keywords: graph, drawing, path, crossing number, join product.
2010 Mathematics Subject Classification: 05C10, 05C38.
References
Received 30 November 2009
Revised 22 June 2010
Accepted 28 June 2010
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