Resumen de An upper bound on the basis number of the powers of the complete graphs

Salar Y. Alsardary

• The basis number of a graph G is defined by Schmeichel to be the least integer h such that G has an h-fold basis for its cycle space. MacLane showed that a graph is planar if and only if its basis number is ≤. Schmeichel proved that the basis number of the complete graph K n is at most 3>. We generalize the result of Schmeichel by showing that the basis number of the d-th power of K n is at most 2d+1.