The Spectrum of de Bruijn and Kautz Graphs

We give here a complete description of the spectrum of de Bruijn and Kautz graphs. It is well known that spectral techniques have proved to be very useful tools to study graphs, and we give some examples of application of our result, by deriving tight bounds on the expansion parameters of those graphs.

[1]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[2]  Michael Doob,et al.  Spectra of graphs , 1980 .

[3]  Mark Jerrum,et al.  Approximate Counting, Uniform Generation and Rapidly Mixing Markov Chains , 1987, International Workshop on Graph-Theoretic Concepts in Computer Science.

[4]  Marie-Claude Heydemann,et al.  On forwarding indices of networks , 1989, Discret. Appl. Math..

[5]  Noga Alon,et al.  Eigenvalues and expanders , 1986, Comb..

[6]  Dhiraj K. Pradhan,et al.  Fault-Tolerant Multiprocessor Link and Bus Network Architectures , 1994, IEEE Transactions on Computers.

[7]  Patrick Solé,et al.  Expanding and Forwarding , 1995, Discret. Appl. Math..

[8]  Jean-Claude Bermond,et al.  Large fault-tolerant interconnection networks , 1989, Graphs Comb..

[9]  Samuel Dolinar,et al.  A VLSI decomposition of the deBruijn graph , 1989, JACM.

[10]  Abraham Lempel,et al.  On a Homomorphism of the de Bruijn Graph and its Applications to the Design of Feedback Shift Registers , 1970, IEEE Transactions on Computers.

[11]  Denis Trystram,et al.  Parallel algorithms and architectures , 1995 .

[12]  Prabir Bhattacharya Decomposition of de Bruijn graphs , 1990 .

[13]  S. Louis Hakimi,et al.  Fault-Tolerant Routing in DeBruijn Comrnunication Networks , 1985, IEEE Transactions on Computers.

[14]  Bojan Mohar,et al.  Isoperimetric numbers of graphs , 1989, J. Comb. Theory, Ser. B.

[15]  H. Fredricksen A Survey of Full Length Nonlinear Shift Register Cycle Algorithms , 1982 .