Discussiones Mathematicae Graph Theory 31(2) (2011) 321-331
doi: 10.7151/dmgt.1548

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THE CROSSING NUMBERS OF JOIN PRODUCTS OF PATHS WITH GRAPHS OF ORDER FOUR

Marián Klešč and  Stefan Schrötter

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

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.

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Received 30 November 2009
Revised 22 June 2010
Accepted 28 June 2010