A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
On forwarding indices of networks
Discrete Applied Mathematics
Addressing, Routing, and Broadcasting in Hexagonal Mesh Multiprocessors
IEEE Transactions on Computers
Group action graphs and parallel architectures
SIAM Journal on Computing
Performance Analysis of Virtual Cut-Through Switching in HARTS: A Hexagonal Mesh Multicomputer
IEEE Transactions on Computers
New methods for using Cayley graphs in interconnection networks
Discrete Applied Mathematics - Special double volume: interconnection networks
Regular maps from Cayley graphs, part 1: balanced Cayley maps
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
The edge-forwarding index of orbital regular graphs
Discrete Mathematics
Distributed loop computer networks: a survey
Journal of Parallel and Distributed Computing
On orbital regular graphs and Frobenius graphs
Discrete Mathematics - Special issue on Graph theory
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
A Combinatorial Problem Related to Multimodule Memory Organizations
Journal of the ACM (JACM)
Complete rotations in Cayley graphs
European Journal of Combinatorics
A complementary survey on double-loop networks
Theoretical Computer Science
Skew-morphisms of regular Cayley maps
Discrete Mathematics - Algebraic and topological methods in graph theory
Gossiping in Cayley Graphs by Packets
Selected papers from the 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics and Computer Science
A survey on multi-loop networks
Theoretical Computer Science
Graph Theory
A Class of Arc-Transitive Cayley Graphs as Models for Interconnection Networks
SIAM Journal on Discrete Mathematics
Efficient Communication Algorithms in Hexagonal Mesh Interconnection Networks
IEEE Transactions on Parallel and Distributed Systems
Gossiping and routing in second-kind Frobenius graphs
European Journal of Combinatorics
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A Frobenius group is a transitive permutation group which is not regular but only the identity element can fix two points. Such a group can be expressed as the semidirect product G=K@?H of a nilpotent normal subgroup K and another group H fixing a point. A first-kind G-Frobenius graph is a connected Cayley graph on K with connection set an H-orbit a^H on K that generates K, where H has an even order or a is an involution. It is known that the first-kind Frobenius graphs admit attractive routing and gossiping algorithms. A complete rotation in a Cayley graph on a group G with connection set S is an automorphism of G fixing S setwise and permuting the elements of S cyclically. It is known that if the fixed-point set of such a complete rotation is an independent set and not a vertex-cut, then the gossiping time of the Cayley graph (under a certain model) attains the smallest possible value. In this paper we classify all first-kind Frobenius circulant graphs that admit complete rotations, and describe a means to construct them. This result can be stated as a necessary and sufficient condition for a first-kind Frobenius circulant to be 2-cell embeddable on a closed orientable surface as a balanced regular Cayley map. We construct a family of non-Frobenius circulants admitting complete rotations such that the corresponding fixed-point sets are independent and not vertex-cuts. We also give an infinite family of counterexamples to the conjecture that the fixed-point set of every complete rotation of a Cayley graph is not a vertex-cut.