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Line digraph iterations and connectivity analysis of de Bruijn and Kautz graphs

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3 Author(s)
Ding-Zhu, D. ; Dept. of Comput. Sci., Minnesota Univ., Minneapolis, MN, USA ; Yuh-Dauh Lyuu ; Hsu, D.F.

A graph has spread (m, k, l) if for any m+1 distinct nodes x, y1, . . ., ym and m positive integers r1 , . . ., rm, such that Σiri=k, there exist k node-disjoint paths of length at most 1 from x to the yi, where ri of them end at yi. 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, k-diameter, vulnerability, and some other measures related to length-bound disjoint paths

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Computers, IEEE Transactions on  (Volume:42 ,  Issue: 5 )