Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Automorphism groups, isomorphism, reconstruction
Handbook of combinatorics (vol. 2)
Journal of Computer and System Sciences
On finite groups with the Cayley isomorphism property
Journal of Graph Theory
Symmetries and sense of direction in labeled graphs
Discrete Applied Mathematics
Complexity of Deciding Sense of Direction
SIAM Journal on Computing
Sense of Direction in Distributed Computing
DISC '98 Proceedings of the 12th International Symposium on Distributed Computing
Sorting and Searching on the Word RAM
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
On the nlog n isomorphism technique (A Preliminary Report)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Isomorphic Cayley graphs on nonisomorphic groups
Journal of Graph Theory
Weak sense of direction labelings and graph embeddings
Discrete Applied Mathematics
Testing set proportionality and the Ádám isomorphism of circulant graphs
Journal of Discrete Algorithms
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Given a class C of Cayley graphs, and given an edge-colored graph G of n vertices and m edges, we are interested in the problem of checking whether there exists an isomorphism Φ preserving the colors such that G is isomorphic by Φ to a graph in C colored by the elements of its generating set. In this paper, we give an O(m log n)-time algorithm to check whether G is color-isomorphic to a Cayley graph, improving a previous O(n4.752 log n) algorithm. In the case where C is the class of the Cayley graphs defined on Abelian groups, we give an optimal O(m)-time algorithm. This algorithm can be extended to check color-isomorphism with Cayley graphs on Abelian groups of given rank. Finally, we propose an optimal O(m)-time algorithm that tests color-isomorphism between two Cayley graphs on Zn, i.e., between two circulant graphs. This latter algorithm is extended to an optimal O(n)-time algorithm that tests color-isomorphism between two Abelian Cayley graphs of bounded degree.