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

• Autores: Salar Y. Alsardary
• Localización: Czechoslovak mathematical journal, ISSN 0011-4642, Vol. 51, Nº 2, 2001, págs. 231-238
• Idioma: inglés
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• Resumen

  • 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.