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Independence Number, Neighborhood Intersection and Hamiltonian Properties

Author(s): Fan Yunzheng

Journal: Boletim da Sociedade Paranaense de Matemática
ISSN 0037-8712

Volume: 22;
Issue: 2;
Start page: 43;
Date: 2004;
Original page

Keywords: Independence number | Neighborhood | Cycle.

Let G be a 2-connected simple graph of order n with the independencenumber alpha. We show here that forall u; v in V(G) and any z in {u,v}, win V(G){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.
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