Abstract:

A graph G is a P₃-dominated graph if J(x,y)∪J′(x,y)≠Φ for any pair of vertices x and y of d(x,y)=2.This paper proves that for any pair of nonadjacent vertices x and y in G,which is a 2-connected P₃-dominated graph of order n no less than 3, if 2|N(x)∪N(y)|+d(x)+d(y)≥2n-5, then G has a Hamilton cycle or G∈{K_2,3,K_1,1,3}.

Key words: quasi-claw-free graphs, P₃-dominated graphs, Hamilton cycle