Embedding K2,3,m Graphs on Torus
Abstract
This script aim to determine the maximal value of m of K2,3,m graph so that can be redrawn on torus without intersection of edges. Hereinafter, will be determined the toroidal crossing number of K2,3,m which nontoroidal by the m minimize. To determined if the K2,3,m graph is toroidal, it is enough with drawn the graph on torus without intersection of edges, whereas, to determined if it is nontoroidal, besides with drawn, is also needed by theorem about properties of graph that containing K5-subdivision. Then to determined the toroidal crossing number was used the technique by proof of the crossing number of K2,2,3 and looked for of all probabilities of the edges is going to intersect. In this research, was obtained the result that maximal value of m of K2,3,m so that can be drawn on torus without intersection of edges is 3, while the toroidal crossing number of K2,3,4 is 2, and our conjecture is tcr().
