A survey: Hamiltonian cycles in Cayley graphs

DOI10.1016/0012-365X(84)90010-4zbMath0718.05038MaRDI QIDQ5925238

Joseph A. Gallian, Dave Witte Morris

Publication date: 1984

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

surveyCayley graphsHamiltonian cyclesdigraphs

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Directed graphs (digraphs), tournaments (05C20) Eulerian and Hamiltonian graphs (05C45)

Related Items (25)

Cayley graphs of order 6pq and 7pq are Hamiltonian ⋮ Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian ⋮ Graphs that admit square 1-factorizations are hamiltonian Cayley graphs ⋮ Hamiltonian cycles and decompositions of Cayley digraphs of finite Abelian groups ⋮ Infinite circulants and their properties ⋮ The diameters of almost all Cayley digraphs ⋮ Isomorphisms of circulant digraphs of degree 3 ⋮ On Hamilton decompositions of infinite circulant graphs ⋮ Dead ends on wreath products and lamplighter groups ⋮ Cayley graphs of order kp are hamiltonian for k < 48 ⋮ Hamilton cycles in dense vertex-transitive graphs ⋮ Circuits on directed grids ⋮ On minimal generating sets for symmetric and alternating groups ⋮ Almost all Cayley graphs are hamiltonian ⋮ Chip firing on Dynkin diagrams and McKay quivers ⋮ Hamilton circles in Cayley graphs ⋮ Cayley graphs on groups with commutator subgroup of order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2</mml:mn><mml:mi>p</mml:mi></mml:math> are hamiltonian ⋮ Hamilton decompositions of one-ended Cayley graphs ⋮ Cayley digraphs of prime-power order are hamiltonian ⋮ Infinite circulant digraphs and random infinite circulant digraphs ⋮ Hamiltonian decomposition of Cayley graphs of orders \(p^2\) and \(pq\) ⋮ A survey on Hamiltonicity in Cayley graphs and digraphs on different groups ⋮ Miscellaneous Digraph Classes ⋮ On a relationship between Cayley graphs and \(G\)-graphs with some applications ⋮ Hamiltonian cycles of power graph of abelian groups

Cites Work

• Hamiltonian circuits in Cayley graphs
• Connected Cayley graphs of semi-direct products of cyclic groups of prime order by Abelian groups are Hamiltonian
• Infinite Hamiltonian paths in Cayley digraphs
• On Hamiltonian cycles in Cayley graphs of wreath products
• On hamiltonian circuits in Cayley diagrams
• Enumeration of Hamiltonian paths in Cayley diagrams
• The conjunction of Cayley digraphs
• On Hamiltonian circuits in Cartesian products of Cayley digraphs
• Partial products in finite groups
• Hamiltonian cycles in generalized Petersen graphs
• Paths and circuits in finite groups
• Hamiltonian circuits in some maps on the torus
• When the cartesian product of two directed cycles is hypo-Hamiltonian
• Hamiltonian groups are color-graph-hamiltonian
• Exceptional trivalent cayley graphs for dihedral groups
• On Hamiltonian Cycles in Metacirculant Graphs
• Hamiltonian cycles in cayley color graphs
• Hamiltonian Decompositions of Graphs, Directed Graphs and Hypergraphs
• When the cartesian product of directed cycles is Hamiltonian
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