a b s t r a c tThere are only few results concerning crossing numbers of join of some graphs. In the paper, for the special graph H on six vertices we give the crossing numbers of its join with n isolated vertices as well as with the path P n on n vertices and with the cycle C n .
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.
In this article we determine the crossing numbers of the Cartesian products of graphs on four vertices with paths and stars.The crossing number v(G) of a graph G is the minimum number of "crossings" in any "good" drawing of G in the plane. By a drawing of G in the plane Il we mean a collection of points P in Il and open arcs A in Il -P for which there are correspondences between V and P and between
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