Abstract
A Hamiltonian graph G = ( V,E ) is called hyper-Hamiltonian if G - v is Hamiltonian for any v ∈ V ( G ). G is called a circulant if its automorphism group contains a | V ( G )|-cycle. First, we give the necessary and sufficient conditions for any undirected connected circulant to be hyper-Hamiltonian. Second, we give necessary and sufficient conditions for a connected circulant digraph with two jumps to be hyper-Hamiltonian. In addition, we specify some sufficient conditions for a circulant digraph with arbitrary number of jumps to be hyper-Hamiltonian.
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