Abstract
A graph G is called triangle-free if G has no induced K 3 as a subgraph. We set σ 3= min{∑ i=1 3 d(v i)|{v 1,v 2,v 3} is an independent set of vertices in G}. In this paper, we show that if G is a 1-tough and triangle-free graph of order n with n⩽ σ 3, then G is hamiltonian.
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