Design theory
Topological graph theory
Isomorphism problem for relational structures with a cyclic automorphism
European Journal of Combinatorics
Isomorphisms of Cayley multigraphs of degree 4 on finite Abelian groups
European Journal of Combinatorics
A non-Cayley-invariant Cayley graph of the elementary Abelian group of order 64
Discrete Mathematics
Half-Transitive Graphs of Prime-Cube Order
Journal of Algebraic Combinatorics: An International Journal
A´da´m's conjecture is true in the square-free case
Journal of Combinatorial Theory Series A
The isomorphism problem for Cayley digraphs on groups of prime-squared order
Discrete Mathematics
Isomorphism problem for Cayley graphs of Z3p
Discrete Mathematics
Automorphism groups, isomorphism, reconstruction
Handbook of combinatorics (vol. 2)
Handbook of combinatorics (vol. 2)
On Ádám's conjecture for circulant graphs
Discrete Mathematics
The cyclic groups with the m-DCI property
European Journal of Combinatorics
On isomorphisms of connected Cayley graphs
Discrete Mathematics
On orbital regular graphs and Frobenius graphs
Discrete Mathematics - Special issue on Graph theory
Automorphism groups and isomorphisms of Cayley digraphs
Discrete Mathematics - Special issue on Graph theory
On the isomorphism problem of Cayley graphs of Abelian groups
Discrete Mathematics
On finite groups with the Cayley isomorphism property
Journal of Graph Theory
Isomorphisms of finite Cayley digaphs of bounded valency
Journal of Combinatorial Theory Series B
On isomorphisms of connected Cayley graphs, II
Journal of Combinatorial Theory Series B
On Cayley Graphs of Abelian Groups
Journal of Algebraic Combinatorics: An International Journal
On isomorphisms of finite Cayley graphs
European Journal of Combinatorics
On the isomorphism problem for finite Cayley graphs of bounded valency
European Journal of Combinatorics
Isomorphisms of finite Cayley digraphs of bounded valency, II
Journal of Combinatorial Theory Series A
On finite groups with the Cayley Isomorphism property, II
Journal of Combinatorial Theory Series A
Elementary proofs that Z2p and Z3p are CI-groups
European Journal of Combinatorics - In memoriam François Jaeger
On half-transitive metacirculant graphs of prime-power order
Journal of Combinatorial Theory Series B
An elementary Abelian group of rank 4 is a CI-Group
Journal of Combinatorial Theory Series A
On the isomorphisms of Cayley graphs of Abelian groups
Journal of Combinatorial Theory Series B
On cubic Cayley graphs of finite simple groups
Discrete Mathematics - Algebraic and topological methods in graph theory
An elementary Abelian group of large rank is not a CI-group
Discrete Mathematics - The 2000 Com2MaC conference on association schemes, codes and designs
Automorphism Groups of Metacirculant Graphs of Order a Product of Two Distinct Primes
Combinatorics, Probability and Computing
On cubic Cayley graphs of finite simple groups
Discrete Mathematics - Algebraic and topological methods in graph theory
On the Cayley isomorphism problem for ternary relational structures
Journal of Combinatorial Theory Series A
On isomorphisms of abelian Cayley objects of certain orders
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Symmetry properties of chordal rings of degree 3
Discrete Applied Mathematics
Classifying Arc-Transitive Circulants
Journal of Algebraic Combinatorics: An International Journal
Relative difference sets in Alt(5)
Journal of Combinatorial Theory Series A
Relative difference sets fixed by inversion and Cayley graphs
Journal of Combinatorial Theory Series A
Further restrictions on the structure of finite CI-groups
Journal of Algebraic Combinatorics: An International Journal
Elementary Abelian p-groups of rank greater than or equal to 4p -2 are not CI-groups
Journal of Algebraic Combinatorics: An International Journal
On automorphism groups of quasiprimitive 2-arc transitive graphs
Journal of Algebraic Combinatorics: An International Journal
Enumeration of 2-regular circulant graphs and directed double networks
Discrete Applied Mathematics
A classification of nonabelian simple 3-BCI-groups
European Journal of Combinatorics
Classifying a family of edge-transitive metacirculant graphs
Journal of Algebraic Combinatorics: An International Journal
On Cayley digraphs on nonisomorphic 2-groups
Journal of Graph Theory
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The isomorphism problem for Cayley graphs has been extensively investigated over the past 30 years. Recently, substantial progress has been made on the study of this problem, many long-standing open problems have been solved, and many new research problems have arisen. The results obtained, and methods developed in this area have also effectively been used to solve other problems regarding finite vertex-transitive graphs. The methods used in this area range from deep group theory, including the finite simple group classification, through to combinatorial techniques. This article is devoted to surveying results, open problems and methods in this area.