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
HARTS: A Distributed Real-Time Architecture
Computer - Special issue on real-time systems
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
The edge-forwarding index of orbital regular graphs
Discrete Mathematics
Distributed loop computer networks: a survey
Journal of Parallel and Distributed Computing
Hamiltonian cycles and paths in Cayley graphs and digraphs—a survey
Discrete Mathematics
On isomorphisms of connected Cayley graphs
Discrete Mathematics
On orbital regular graphs and Frobenius graphs
Discrete Mathematics - Special issue on Graph theory
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
Complete rotations in Cayley graphs
European Journal of Combinatorics
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
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
Isomorphic Cayley graphs on nonisomorphic groups
Journal of Graph Theory
Modeling Toroidal Networks with the Gaussian Integers
IEEE Transactions on Computers
A Class of Arc-Transitive Cayley Graphs as Models for Interconnection Networks
SIAM Journal on Discrete Mathematics
The Topology of Gaussian and Eisenstein-Jacobi Interconnection Networks
IEEE Transactions on Parallel and Distributed Systems
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
Perfect Codes for Metrics Induced by Circulant Graphs
IEEE Transactions on Information Theory
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A Frobenius group is a transitive but not regular permutation group such that only the identity element can fix two points. A finite Frobenius group can be expressed as G=K@?H with K a nilpotent normal subgroup. A first-kind G-Frobenius graph is a Cayley graph on K with connection set S an H-orbit on K generating K, where H is of even order or S consists of involutions. We classify all 6-valent first-kind Frobenius circulant graphs such that the underlying kernel K is cyclic. We give optimal gossiping and routing algorithms for such a circulant and compute its forwarding indices, Wiener indices and minimum gossip time. We also prove that its broadcasting time is equal to its diameter plus two or three. We prove that all 6-valent first-kind Frobenius circulants with cyclic kernels are Eisenstein-Jacobi graphs, the latter being Cayley graphs on quotient rings of the ring of Eisenstein-Jacobi integers. We also prove that larger Eisenstein-Jacobi graphs can be constructed from smaller ones as topological covers, and a similar result holds for 6-valent first-kind Frobenius circulants. As a corollary any Eisenstein-Jacobi graph with order congruent to 1 modulo 6 and underlying Eisenstein-Jacobi integer not an associate of a real integer, is a cover of a 6-valent first-kind Frobenius circulant. A distributed real-time computing architecture known as HARTS or hexagonal mesh is a special 6-valent first-kind Frobenius circulant.