Abstract
In 1990 G. T. Chen proved that if G is a 2-connected graph of order n and 2|N(x) ∪ N(y)| + d(x) + d(y) ≥ 2n − 1 for each pair of nonadjacent vertices x, y ∈ V (G), then G is Hamiltonian. In this paper we prove that if G is a 2-connected graph of order n and 2|N(x) ∪ N(y)| + d(x)+d(y) ≥ 2n−1 for each pair of nonadjacent vertices x, y ∈ V (G) such that d(x, y) = 2, then G is Hamiltonian.
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References
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Zhao, K., Lin, Y. & Zhang, P. One sufficient condition for Hamiltonian graphs involving distances. Russ Math. 56, 38–43 (2012). https://doi.org/10.3103/S1066369X12040056
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DOI: https://doi.org/10.3103/S1066369X12040056