Enumerations of the maximum rectilinear crossing numbers of complete and complete multi-partite graphs
Che Sheng Gan, Voon Chet Koo · Journal of Discrete Mathematical Sciences and Cryptography · 2006
The maximum rectilinear crossing number of a complete graph of order n is known to be . In this paper, the edge-set of a complete graph is partitioned into L layers, where the contribution of each layer on the maximum rectilinear crossing number is particularly described. We obtain combinatorial identities and triangular arrays that can be used to calculate . The results obtained from the enumeration of complete graphs are then used to calculate the maximum rectilinear crossing number of the complete multi-partite graphs.