Báo cáo toán học: " Crooked Functions, Bent Functions, and Distance Regular Graphs" pptx

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Ngày tải lên: 05/08/2014, 15:20

... partition V = I ∪K such that the subgraphs G[I] and G[K] of G induced by I and K are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary condition for a spl ... is also true for any k ≥ 6andm>k+2. The proof of Theorem 10 is complete.  References 1. M. Behzad and G. Chartrand, Introduction to the Theory of Graphs, Allyn and Bacon, Boston, 1971....

Ngày tải lên: 06/08/2014, 05:20

... 417-433. [8] T. Brylawski and J. Oxley, The broken-circuit complex: Its structure and factorizations,Eur. J. Comb. 2 (1981), 107-121. [9] T. Brylawski and J. Oxley, The Tutte Polynomial and its Applications, ... antimatroid and let (C, ⊆) be the lattice of convex sets. Then β(A)=−  C∈C µ(∅,C)|C|. Proof. This follows from Theorem 1 of [19] and the definition of β(A). Recall that if...

Ngày tải lên: 07/08/2014, 06:20

... 2-antipodal distance- regular graphs. Finally, Garriga and the author [11] solved the general case, characterizing distance- regular graphs as those regular graphs whose number of vertices at distance ... show that this is also true for r-antipodal distance- regular graphs. As a main result it is shown that an antipodal regular graph is distance- regular if, and only if,...

Ngày tải lên: 07/08/2014, 06:22

... = ∅ and |U|+ |W | = n, there is a vertex v ∈ V − (U ∪ W ) such that all edges between v and U are present and no edges between v and W are present. A graph is strongly regular if it is a regular ... ∅ and |U| + |W | = n there is a vertex v ∈ V − (U ∪ W ) such that all edges between v and U are present and no edges between v and W are present. A strongly regular SR(N,K,Λ,...

Ngày tải lên: 07/08/2014, 06:23

... M. Molloy, R. Robinson and N.C. Wormald, Generating and counting Hamilton cycles in random regular graphs, Journal of Algorithms 21 (1996), 176–198. [6] M. Ghandehari and H. Hatami, Two upper ... Janson, Random regular graphs: asymptotic distributions and contiguity, Combi- natorics, Probability and Computing 4 (1995), pp. 369–405. [9] S. Janson, T. Luczak and A. Ruci´nski, R...

Ngày tải lên: 07/08/2014, 13:21

... 1, joining w to u in G, and thus in H, a contradiction. Hence, u /∈ P (v, w) and, by symmetry, v /∈ P (u, w) . Therefore, the paths P (u, w) and P (v, w) belong to H, and we have dist H (w, u) ... proof. Hereafter, we assume that dist H (w, u) ≥ D and, by symmetry, dist H (w, v) ≥ D. Let P (u, w) and P (v, w) be shortest paths joining u and v to w in G. If u ∈ P (v, w) , then ther...

Ngày tải lên: 07/08/2014, 13:21

... Braunstein, S. Ghosh, T. Mansour, S. Severini and R. C. Wilson, Phys. Rev. A 73 (2006) 012320. [12] R. Hildebrand, S. Mancini and S. Severini, Combinatorial Laplacian and Positivity Under Partial Transpose, ... Ali Saif M. Hassan and Pramod Joag [9] studied the related issues like classification of pure and mixed states, von Neumann entropy, separability of multipartite quantum state...

Ngày tải lên: 07/08/2014, 15:22

... taken with multiplicity 2. Crooked Functions, Bent Functions, and Distance Regular Graphs T.D. Bending D. Fon-Der-Flaass School of Mathematical Sciences, Queen Mary and Westfield College, London ... {(a, i, α)}; vertices (a, i, α )and( b, j, β) are adjacent if and only if they are distinct, and α + β = D(a, i; b, j). PROPOSITION 13 The graph G Q is distance regular with...

Ngày tải lên: 07/08/2014, 06:22

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Ngày tải lên: 05/08/2014, 15:20