Gerenalization of the Well-Known Fan Type Theorem
Kewen Zhao · Systems Engineering · 2004
Let α to be independence number of graph G, in 1984 Fan showed: Let G be a 2-connected graph of order n, for every pair vertices x,y of d(x,y)=2, if max{d(x),d(y)}≥n/2, then G is Hamiltonian. In the paper we prove: Let G be a 2-connected graph of order n, for every pair of distinct nonadjacent vertices x and y with 1≤|N(x)∩N(y)|≤α-1, if max{d(x),d(y)}≥n/2, then G is Hamiltonian.