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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Zbigniew R. Bogdanowicz
US Army, CCDC Armaments Center, Picatinny, New Jersey 07806, USA
Electrical & Electronics Engineering

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Hyper-Hamiltonian circulants Zbigniew R. Bogdanowicz
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.1.16

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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