The server is under maintenance between 08:00 to 12:00 (GMT+08:00), and please visit later.
We apologize for any inconvenience caused
Login  | Sign Up  |  Oriprobe Inc. Feed
China/Asia On Demand
Journal Articles
Laws/Policies/Regulations
Companies/Products
Bookmark and Share
essential independent condition for graphs to be hamiltonian
Author(s): 
Pages: 184-190
Year: Issue:  2
Journal: Engineering Sciences

Keyword:  GetLinkList(KeywordFilter('new sufficient conditions Hamiltonian graphs cycles')'kw''CJFQ');
Abstract: Let G be a graph of order n. For graph to be Hamiltonian, beginning with Dirac's classic result in 1952, Dirac's theorem was followed by that of Ore in 1960. In 1984, Fan generalized Dirac's theorem and Ore's theorem as if G is a 2-connected graph of order n and max {d (u),d (v)}≥n/2 for each pair of vertices u and v with d (u,v)=2, then G is hamiltonian. In 1991, Faudree et al proved that if G is a 2-connected graph and, |N (u)∪N (v)|+δ(G)≥n for each pair of nonadjacent vertices u,v∈V(G), then G is hamiltonian. This paper generalizes the above conditions of Dirac, Ore, Fan and Faudree et al in the case of 3-connected graph and proves that if G is a 3-connected graph of order n and max{|N(x)∪ N (y)| +d (u), |N (w)∪N (z)|+d (v)}≥n for every choice of 6 Essential independent vertices, then G is hamiltonian.
Related Articles
No related articles found