Abstract
It is proved that the hamiltonian index of a connected graph other than a path is less than its diameter which improves the results of P. A. Catlin etc. [J. Graph Theory 14 (1990) 347–364] and M. L. Sarazin [Discrete Math. 134(1994)85–91]. Nordhaus-Gaddum's inequalities for the hamiltonian index of a graph are also established.
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