A survey on Hamiltonicity in Cayley graphs and digraphs on different groups

DOI10.1142/S1793830919300029zbMath1426.05085OpenAlexW2969633698WikidataQ127350628 ScholiaQ127350628MaRDI QIDQ5242819

G. H. J. Lanel, J. K. Ratnayake, B. A. K. Welihinda, S. Thevasha, H. K. Pallage

Publication date: 7 November 2019

Published in: Discrete Mathematics, Algorithms and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793830919300029

zbMATH Keywords

Cayley graphHamiltonian cyclesCayley digraphHamiltonian pathsvertex-transitive graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Eulerian and Hamiltonian graphs (05C45)

Related Items (3)

Loopless algorithms to generate maximum length Gray cycles wrt. \(k\)-character substitutions ⋮ Unnamed Item ⋮ Dead ends on wreath products and lamplighter groups

Cites Work

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• Cayley graphs of order \(27p\) are Hamiltonian
• Lifting Hamilton cycles of quotient graphs
• Hamiltonian cycles in cubic Cayley graphs: The \(\langle 2,4k,3\rangle \) case
• Hamiltonian cycles in (2,3,c)-circulant digraphs
• Hamiltonian paths in Cayley graphs
• Connected Cayley graphs of semi-direct products of cyclic groups of prime order by Abelian groups are Hamiltonian
• Hamiltonian decomposition of Cayley graphs of degree 4
• Paths and circuits in finite groups
• Hamiltonian decompositions of Cayley graphs on abelian groups of even order
• Hamiltonian paths in Cartesian powers of directed cycles
• Cayley graphs of order \(30p\) are Hamiltonian
• Gray codes for reflection groups
• Hamiltonian decompositions of Cayley graphs on abelian groups of odd order
• Hamiltonian cycles and paths in Cayley graphs and digraphs---a survey
• On Cayley digraphs that do not have Hamiltonian paths
• Vertex-transitive digraphs of order \(p^5\) are Hamiltonian
• Hamiltonian cycles in Cayley graphs of imprimitive complex reflection groups
• Hamiltonicity of cubic Cayley graphs
• Hamiltonian cycles in Cayley graphs whose order has few prime factors
• Cayley graphs on nilpotent groups with cyclic commutator subgroup are hamiltonian
• Hyper hamiltonian laceability of Cayley graphs generated by transpositions
• Hamilton paths in Cayley graphs on generalized dihedral groups
• When the cartesian product of directed cycles is Hamiltonian
• On non-Hamiltonian circulant digraphs of outdegree three
• On Hamilton decompositions of infinite circulant graphs
• Almost all Cayley graphs are hamiltonian
• Cayley graphs of order 16p are hamiltonian
• On Some Structural Properties of Star and Pancake Graphs
• Hamiltonian properties on a class of circulant interconnection networks
• Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian
• A new class of interconnection networks based on the alternating group
• 2-generated Cayley digraphs on nilpotent groups have hamiltonian paths
• Hamilton paths in Cayley graphs on Coxeter groups: I
• A survey: Hamiltonian cycles in Cayley graphs
• Hamilton-connected Cayley graphs on Hamiltonian groups

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