Hyper-Hamiltonian circulants

Zbigniew R. Bogdanowicz


A Hamiltonian graph G = (V,E) is called hyper-Hamiltonian if G-v is Hamiltonian for any vV(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.


Hyper-hamiltonian graph, Hamilton cycle, circulant, Hamiltonian graph

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DOI: http://dx.doi.org/10.5614/ejgta.2021.9.1.16


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