Distance distribution of nodes in star graphs

Abstract The purpose of the work is to provide a solution to the long-standing problem of computing the distance distribution among the nodes in a star graph, i.e., computing the exact number of nodes at a distance k from the identity node in a star graph where k varies from 0 to the diameter of the graph. A star graph is a Cayley graph like a hypercube; for a hypercube Q n , there are exactly n r nodes at a distance r from the identity node where r varies from 0 to n .

[1]  Shahram Latifi,et al.  Transposition Networks as a Class of Fault-Tolerant Robust Networks , 1996, IEEE Trans. Computers.

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

[3]  Dilip Sarkar,et al.  Optimal Broadcasting on the Star Graph , 1992, IEEE Trans. Parallel Distributed Syst..

[4]  Shahram Latifi,et al.  Conditional Fault Diameter of Star Graph Networks , 1996, J. Parallel Distributed Comput..

[5]  Sajal K. Das,et al.  Book Review: Introduction to Parallel Algorithms and Architectures : Arrays, Trees, Hypercubes by F. T. Leighton (Morgan Kauffman Pub, 1992) , 1992, SIGA.

[6]  M. H. Schultz,et al.  Topological properties of hypercubes , 1988, IEEE Trans. Computers.

[7]  C. T. Howard Ho,et al.  Optimal Broadcasting on SIMD Hypercubes without Indirect Addressing Capability , 1991, J. Parallel Distributed Comput..

[8]  Khaled Day,et al.  A Comparative Study of Topological Properties of Hypercubes and Star Graphs , 1994, IEEE Trans. Parallel Distributed Syst..

[9]  Pradip K. Srimani,et al.  Fault Diameter of Star Graphs , 1993, Inf. Process. Lett..

[10]  Sheldon B. Akers,et al.  The Star Graph: An Attractive Alternative to the n-Cube , 1994, ICPP.

[11]  Selim G. Akl,et al.  A Parallel Algorithm for Computing Fourier Transforms on the Star Graph , 1994, IEEE Trans. Parallel Distributed Syst..

[12]  Selim G. Akl,et al.  On Some Properties and Algorithms for the Star and Pancake Interconnection Networks , 1994, J. Parallel Distributed Comput..

[13]  S. Lakshmivarahan,et al.  Symmetry in Interconnection Networks Based on Cayley Graphs of Permutation Groups: A Survey , 1993, Parallel Comput..