The Geng-Hua Fan conditions for pancyclic or Hamilton-connected graphs
Journal of Combinatorial Theory Series B
Graph Theory With Applications
Graph Theory With Applications
On Hamiltonian cycles and Hamiltonian paths
Information Processing Letters
Normal eulerian clique-covering and hamiltonicity
Information Processing Letters
On the 1-fault hamiltonicity for graphs satisfying Ore's theorem
Information Processing Letters
| Hi-index | 0.89 |
Rahman and Kaykobad proved the following theorem on Hamiltonian paths in graphs. Let G be a connected graph with n vertices. If d(u)+d(v)+@d(u,v)=n+1 for each pair of distinct non-adjacent vertices u and v in G, where @d(u,v) is the length of a shortest path between u and v in G, then G has a Hamiltonian path. It is shown that except for two families of graphs a graph is Hamiltonian if it satisfies the condition in Rahman and Kaykobad's theorem. The result obtained in this note is also an answer for a question posed by Rahman and Kaykobad.