New results for the degree/diameter problem

The results of computer searches for large graphs with given (small) degree and diameter are presented. The new graphs are Cayley graphs of semidirect products of cyclic groups and related groups. One fundamental use of our “dense graphs” is in the design of efficient communication network topologies. © 1994 by John Wiley & Sons, Inc.

[1]  Lowell Campbell,et al.  Dense Group Networks , 1992, Discret. Appl. Math..

[2]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[3]  Charles Delorme,et al.  Table of Large (Delta, D)-Graphs , 1992, Discret. Appl. Math..

[4]  Gunnar E. Carlsson,et al.  Interconnection Networks Based on a Generalization of Cube-Connected Cycles , 1985, IEEE Transactions on Computers.

[5]  J.W. Moore,et al.  Small Diameter Symmetric Networks from Linear Groups , 1992, IEEE Trans. Computers.

[6]  Paul Erdös,et al.  Maximum degree in graphs of diameter 2 , 1980, Networks.

[7]  R. M. Storwick,et al.  Improved Construction Techniques for (d, k) Graphs , 1970, IEEE Transactions on Computers.

[8]  Karl W. Doty,et al.  New Designs for Dense Processor Interconnection Networks , 1984, IEEE Transactions on Computers.

[9]  E. Bannai,et al.  On finite Moore graphs , 1973 .

[10]  Sheldon B. Akers,et al.  On Group Graphs and Their Fault Tolerance , 1987, IEEE Transactions on Computers.

[11]  Miguel Angel Fiol,et al.  On large (Delta, D)-graphs , 1993, Discret. Math..

[12]  Tatsuro Ito,et al.  Regular graphs with excess one , 1981, Discret. Math..

[13]  Sheldon B. Akers,et al.  A Group-Theoretic Model for Symmetric Interconnection Networks , 1989, IEEE Trans. Computers.

[14]  Bernard Elspas,et al.  Topological constraints on interconnection-limited logic , 1964, SWCT.

[15]  R. M. Damerell.  On Moore graphs , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  Charles Delorme,et al.  Tables of Large Graphs with Given Degree and Diameter , 1982, Inf. Process. Lett..

[17]  G. Sabidussi.  Vertex-transitive graphs , 1964 .

[18]  Paul R. Hafner.  Large Cayley Graphs and Digraphs with Small Degree and Diameter , 1995 .

[19]  F. Comellas,et al.  New large graphs with given degree and diameter , 1994, math/9411218.

[20]  J. A.,et al.  On Moore Graphs with Diameters 2 and 3 , 2022 .

[21]  Reuven Bar-Yehuda,et al.  Connections Between two Cycles - a New Design of Dense Processor Interconnection Networks , 1992, Discret. Appl. Math..

[22]  Charles Delorme,et al.  Strategies for Interconnection Networks: Some Methods from Graph Theory , 1986, J. Parallel Distributed Comput..

[23]  Alan J. Hoffman,et al.  On Moore Graphs with Diameters 2 and 3 , 1960, IBM J. Res. Dev..