Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Hamiltonian cycles and Hamiltonian paths
Information Processing Letters
Graph Theory With Applications
Graph Theory With Applications
A new sufficient condition for Hamiltonicity of graphs
Information Processing Letters
An efficient condition for a graph to be Hamiltonian
Discrete Applied Mathematics
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In 2005, Rahman and Kaykobad proved that if G is a connected graph of order n such that d(x)+d(y)+d(x,y)=n+1 for each pair x, y of distinct nonadjacent vertices in G, where d(x,y) is the length of a shortest path between x and y in G, then G has a Hamiltonian path [Inform. Process. Lett. 94 (2005) 37-41]. In 2006 Li proved that if G is a 2-connected graph of order n=3 such that d(x)+d(y)+d(x,y)=n+2 for each pair x,y of nonadjacent vertices in G, then G is pancyclic or G=K"n"/"2","n"/"2 where n=4 is an even integer [Inform. Process. Lett. 98 (2006) 159-161]. In this work we prove that if G is a 2-connected graph of order n such that d(x)+d(y)+d(x,y)=n+1 for all pairs x, y of distinct nonadjacent vertices in G, then G is pancyclic or G belongs to one of four specified families of graphs.