The forwarding index of communication networks
IEEE Transactions on Information Theory
On forwarding indices of networks
Discrete Applied Mathematics
Discrete Applied Mathematics - Special double volume: interconnection networks
Methods and problems of communication in usual networks
Proceedings of the international workshop on Broadcasting and gossiping 1990
A study of minimum gossip graphs
Discrete Mathematics
Recursive circulants and their embeddings among hypercubes
Theoretical Computer Science
On the structure of minimum broadcast digraphs
Theoretical Computer Science
Algebraic Constructions of Efficient Broadcast Networks
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Families of Graphs Having Broadcasting and Gossiping Properties
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
Gossiping and routing in second-kind Frobenius graphs
European Journal of Combinatorics
Frobenius circulant graphs of valency six, Eisenstein-Jacobi networks, and hexagonal meshes
European Journal of Combinatorics
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Knödel graphs of even order n and degree 1 ≤ Δ ≤ ⌊log2(n)⌋, WΔ,n, are graphs which have been introduced some 25 years ago as the topology underlying a time optimal algorithm for gossiping among n nodes (Discrete Math. 13 (1975) 95). However, they have been formally defined only 7 years ago (Networks 38 (2001) 150). Since then, they have been widely studied as interconnection networks, mainly because of their good properties in terms of broadcasting and gossiping (Int. J. Foundations Comput. Sci. 8(2) (1997) 109, Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science, Vol. 1517, Smolenice, LNCS, 1998, p.63). In particular, Knödel graphs of order 2k, and of degree k, are among the three most popular families of interconnection networks in the literature, along with the hypercube of dimension k, Hk (Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes, Morgan Kaufman Publisher, Los Altos, CA, 1992), and with the recursive circulant graph G(2k, 4) introduced by Park and Chwa in 1994 (Proceedings of the International Symposium on Parallel Architectures, Algorithms and Networks, ISPAN'94, Kanazawa, Japan, 1994, p. 73). Indeed, those three families are commonly presented as good topologies for multicomputer networks, and are comparable since they have the same number of nodes and the same degree.In this paper, we first survey the different results that exist concerning Knödel graphs, mostly in terms of broadcasting and gossiping. We complete this survey by a study of graph-theoretical properties of the "general" Knödel graph WΔ, n, for any even n and 1 ≤ Δ ≤ ⌊log2 (n)⌋. Finally, we propose a rather complete study of Knödel graphs Wk,2k, which allows to compare this topology to the hypercube of dimension k, Hk, and the recursive circulant graph G(2k, 4). We also provide a study of the different embeddings that can exist between any two of these topologies.