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DingZhu Du, Y.D. Lyuu, D.F. Hsu, "Line Digraph Iterations and Connectivity Analysis of de Bruijn and Kautz Graphs," IEEE Transactions on Computers, vol. 42, no. 5, pp. 612616, May, 1993.  
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@article{ 10.1109/12.223681, author = {DingZhu Du and Y.D. Lyuu and D.F. Hsu}, title = {Line Digraph Iterations and Connectivity Analysis of de Bruijn and Kautz Graphs}, journal ={IEEE Transactions on Computers}, volume = {42}, number = {5}, issn = {00189340}, year = {1993}, pages = {612616}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.223681}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Computers TI  Line Digraph Iterations and Connectivity Analysis of de Bruijn and Kautz Graphs IS  5 SN  00189340 SP612 EP616 EPD  612616 A1  DingZhu Du, A1  Y.D. Lyuu, A1  D.F. Hsu, PY  1993 KW  de Bruijn digraphs; digraph iterations; connectivity analysis; Kautz graphs; nodedisjoint paths; graph theory; optimal general theorem; optimal bounds; lengthbound disjoint paths; directed graphs; iterative methods. VL  42 JA  IEEE Transactions on Computers ER   
A graph has spread (m, k, l) if for any m+1 distinct nodes x, y/sub 1/, . . ., y/sub m/ and m positive integers r/sub 1/, . . ., r/sub m/, such that Sigma /sub i/r/sub i/=k, there exist k nodedisjoint paths of length at most 1 from x to the y/sub i/, where r/sub i/ of them end at y/sub i/. This concept contains, and is related to many important concepts used in communications and graph theory. The authors prove an optimal general theorem about the spreads of digraphs generated by line digraph iterations. Useful graphs, like the de Bruijn and Kautz digraphs, can be thus generated. The theorem is applied to the de Bruijn and Kautz digraphs to derive optimal bounds on their spreads, which implies previous results and resolves open questions on their connectivity, diameter, kdiameter, vulnerability, and some other measures related to lengthbound disjoint paths.
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