Abstract
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.
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