J-C. Bermond Z. Liu M. Syska. Mean eccentricities of the de Bruijn networks. n 94-02, I3S, aug 1993. submitted to Networks.  Home/Search Document Details and Download
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Routing and Transmitting Problems in de Bruijn Networks - Liu, Sung (1996) Self-citation (Liu) (Correct)
....defined to be vacuous by convention. Now consider any two distinct vertices x = x n Gamma1 ; x n Gamma2 ; Delta Delta Delta ; x 0 ) and y = y n Gamma1 ; y n Gamma2 ; Delta Delta Delta ; y 0 ) in G. We shall use Lemma 1 and Corollary 1 below to characterize P xy , which were established in [3,5,11]. For the sake of completeness, we provide a short proof which is slightly different. Lemma 1 P xy cannot contain either R 1 L 1 R 2 L 2 or L 1 R 1 L 2 R 2 as subpaths. Proof. It suffices to show for R 1 originating from x and P xy = R 1 L 1 R 2 L 2 since P xy = L 1 R 1 L 2 R 2 can be similarly ....
....path in G) The level of a vertex in the tree is defined as the distance from the root to the vertex, where by convention, the root is at level 0. Let k (x) be the width, i.e. the number of vertices at level k in the shortest path trees rooted at vertex x. According to (3.7) and (3. 8) of [3], k (x) 2(d 1) 2 d k Gamma2 ; 1 k n Gamma 1: Therefore, j N h (x) j 1 h X k=1 k (x) 1 2(d 1) 2 d(d Gamma 1) d h Gamma 1) 2(d 1) 2 d(d Gamma 1) d h ; so that j N h (x) j 2(d 1) 2 d(d Gamma 1) d h ; which implies that s X i=1 j N t Gammai ....
J.C. Bermond, Z. Liu and M. Syska, "Mean eccentricities of de Bruijn networks," Rapport de Recherche INRIA, no. 2114, 1993.
Lower bounds on broadcasting time of de Bruijn type networks - Perennes (1995) (Correct)
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J-C. Bermond Z. Liu M. Syska. Mean eccentricities of the de Bruijn networks. n 94-02, I3S, aug 1993. submitted to Networks.
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