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- Title
On Hamiltonian and Pancyclic Graph.
- Authors
Zhang Jiaxiu, Bijan; Li Weixiao, Bijan
- Abstract
Let G be a connected graph with γ ≥ 3 for ν ∈ V(G). We define N[subk](ν) = {u|u ∈ V(G) and d(u, ν) = k}. It is proved that for each vertex ν ∈ V(G) and each independent set S ⊆ N[sub2](ν), if |N(S) ∩ N(ν)| ≥ |s|+1 then G must be a Hamiltonian graph. Several known sufficient conditions for hamiltonian graphs follow as the corollaries of the above result. It is also noted that for each vertex ν ∈ V(G) and each independent set S ⊆ N[sub2](ν), if |N(S) ∩ N(ν)| ≥ |s|+2, then G is pancyclic.
- Subjects
HAMILTONIAN graph theory; GRAPH theory; COMBINATORICS; MATHEMATICS; ALGEBRA
- Publication
Southeast Asian Bulletin of Mathematics, 2003, Vol 26, Issue 6, p1075
- ISSN
0129-2021
- Publication type
Article