A family of cayley graphs on the hexavalent grid

Discrete Applied Mathematics

Volumn 93, Issue 2-3, 1999, Pages 169-189

  Désérable, Dominique ^a  

^a INSA DE RENNES   (France)

Author keywords

2D hexavalent grid; Arrowhead and diamond; Hierarchical cayley graphs; Iinterconnection networks

Indexed keywords

EID: 0010369313     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00106-7     Document Type: Article

References (22)

1. S.B. Akers, B. Krishnamurthy, A group-theoretic model for symmetric interconnection networks, IEEE Trans. Comput. 38 (4) (1989) 555-566.
2. J.C. Bermond, F. Comellas, D.F. Hsu, Distributed loop computer networks: a survey, J. Parallel Distributed Comput. 24 (1995) 2-10.
3. N. Biggs, Algebraic Graph Theory, Cambridge Univ. Press, London, 1974.
4. M.S. Chen, K.G. Shin, D.D. Kandlur, Addressing, routing, and broadcasting in hexagonal mesh multiprocessors, IEEE Trans. Comput. 39 (1) (1990) 10-18.
5. H.S.M. Coxeter, W.O.J. Moser, Generators and Relations for Discrete Groups, Springer, Berlin, 1957. Fourth ed., 1980.
6. W.J. Dally, C.L. Seitz, The torus routing chip, Distributed Comput. 1 (1986) 187-196.
7. A. Davis, Mayfly - a general-purpose, scalable, parallel processing architecture, J. LISP Symbolic Comput. 5 (1992) 7-47.
8. A.L. Davis, S.V. Robison, The architecture of the FAIM-1 symbolic multiprocessing system, Proceedings of ninth International Joint Conference on Artificial Intelligence, 1985, pp. 32-38.
9. D. Désérable, Broadcasting in the arrowhead torus, Comput. Artif. Intell. 16 (6) (1997) 545-559.
10. D. Désérable, Minimal routing in the triangular grid and in a family of related tori, EuroPar'97, Lecture Notes in Computer Science, vol. 1300, Springer, Berlin, 1997, pp. 218-225.
11. D. Désérable, Arrowhead and diamond diameters, Discrete Appl. Math., submitted for publication.
12. C. Gowrisankaran, Broadcasting on recursively decomposable Cayley graphs, Discrete Appl. Math. 53 (1994) 171-182.
13. I. Grossman, W. Magnus, Groups and their Graphs, New Mathematical Library no 14, Random House, New York, 1964.
14. F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
15. W. Magnus, A. Karrass, D. Solitar, Combinatorial Group Theory: Presentation of Groups in Terms of Generators and Relations, Interscience Publishers, New York, 1966.
16. B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman and Cie, San Francisco, 1982.
17. J. Rattner, The new age of supercomputing, Lecture Notes in Computer Science, vol. 487, Springer, Berlin, 1991, pp. 1-6.
18. J.J. Rotman, The Theory of Groups: an Introduction, Allyn & Bacon, Boston, 1965.
19. Y. Saad, M.H. Schultz, Topological properties of hypercubes, IEEE Trans. Comput. 37 (7) (1988) 867-871.
20. 2 association scheme, Ann. Math. Statist. 30 (1959) 781-798.
21. S.H. Unger, A computer oriented toward spatial problems, Proc. IRE 46 (1958) 1744-1750.
22. J.L. Yebra, M.A. Fiol, P. Morillo, I. Alegre, The diameter of undirected graphs associated to plane tessellations, Ars Combin. 20B (1985) 159-171.