Let G be a 2-connected simple graph of order n with the independence number\alpha. We show here that \forall u; v \in V (G)\backslash\{u,v\} and any z \in \{u,v\}; w \in V (G)\backslash \{u,v\}; with d(w; z) = 2, if |N(u) \ cap N(w)| \geq \alpha - 1 or |N(v) \cap N(w)| \geq \alpha - 1, then G is Hamiltonian, unless G belongs to a kind of special graphs.
@article{7480,
title = {Independence Number, Neighborhood Intersection and Hamiltonian Properties - doi: 10.5269/bspm.v22i2.7480},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v22i2.7480},
language = {EN},
url = {http://dml.mathdoc.fr/item/7480}
}
Yunzheng, Fan. Independence Number, Neighborhood Intersection and Hamiltonian Properties - doi: 10.5269/bspm.v22i2.7480. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v22i2.7480. http://gdmltest.u-ga.fr/item/7480/