The crossing numbers of join products of four graphs of order five with paths and cycles
Michal Staš, Mária Timková · Opuscula Mathematica · 2023
The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane.In the paper, we extend known results concerning crossing numbers of join products of four small graphs with paths and cycles.The crossing numbers of the join products G * + P n and G * + C n for the disconnected graph G * consisting of the complete tripartite graph K 1,1,2 and one isolated vertex are given, where P n and C n are the path and the cycle on n vertices, respectively.In the paper also the crossing numbers of H * + P n and H * + C n are determined, where H * is isomorphic to the complete tripartite graph K 1,1,3 .Finally, by adding new edges to the graphs G * and H * , we are able to obtain crossing numbers of join products of two other graphs G 1 and H 1 with paths and cycles.