Báo cáo toán học: " Hadamard matrices and strongly regular graphs with the 3-e c adjacency property" pdf

... =             C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 2 C 1 C 4 C 3 C 6 C 5 C 8 C 7 C 3 C 4 C 1 C 2 C 7 C 8 C 5 C 6 C 4 C 3 C 2 C 1 C 8 C 7 C 6 C 5 C 5 C 6 C 7 C 8 C 1 C 2 C 3 C 4 C 6 C 5 C 8 C 7 C 2 C 1 C 4 C 3 C 7 C 8 C 5 C 6 C 3 C 4 C 1 C 2 C 8 C 7 C 6 C 5 C 4 C...

Ngày tải lên: 07/08/2014, 06:22

... impose an equivalence relation on two circuits c and c ′ via cyclic permutation. Remark 1. The distinction between cycles and circuits (circuits are cycles which do not have backtracking or tails) ... vertices and by Z l the compo nent with 2 vertices. Similarly, upon removal of the bridge edge f n−2 in the graph L n , we are left with two connected components. We denote...

Ngày tải lên: 08/08/2014, 12:22

... h 3" alt =""

Ngày tải lên: 05/08/2014, 10:20

... whenever C C and C is not a root chain, then there exists a chain π (C) ∈Csuch that starter (C) coversanelementπ s (C) ofπ (C )and terminator (C) is covered by an element π t (C) ofπ (C) . Call such a mapping ... =(A, ≤) and for chain C C, letstarter (C) be the first element of C and let terminator (C) be the last element of C. Call the longest chains in C the ro...

Ngày tải lên: 07/08/2014, 08:20

... order the 2n − 1 one-factors of a one-factorization of the complete graph K 2n in such a way that the union of any two (cyclically) consecutive one-factors is always isomorphic to the same two -regular ... that the difference of consecutive elements is either 1 or α. the electronic journal of combinatorics 12 (2005), #R1 6 Acknowledgements The authors would like to to thank Dan...

Ngày tải lên: 07/08/2014, 08:22

... so we need not consider the case where H is constructed from C 4 and C 6 . First suppose H is constructed from a C 7 (call it C) and a triangle. Let P = C \ {v} and note that each vertex of P ... triangles and a 5-cycle. This time we need not consider the case where H is constructed from a triangle and two copies of C 4 because the independence number of that graph...

Ngày tải lên: 08/08/2014, 14:23

... C 2 , C 3 as follows: • (C 1 ,C 2 ) C 1 if and only if C 2 ∩ C 1 = ∅, • (C 1 ,C 2 ) C 2 if and only if C 2 ∩ C 1 = ∅ and C 2 = C 1 , • (C 1 ,C 2 ) C 3 if and only if C 2 = C 1 . Note that Theorem ... Letting C denote the collection of all r-cycles in K n (considered as sets of edges), E(X 2 r )=  C 1 C  C 2 C P (C 1 C 2 ⊆ G). (2.3) Pa...

Ngày tải lên: 07/08/2014, 08:20

... at the input. Therefore, the following procedure LowDisc basically tries all possible values for ¯ d min and outputs the best bound on the discrepancy discovered in the course of this process. It ... Society 1997 [6] Chung, F., Graham, R.L.: Quasi-random graphs with with given degree sequences. Random Structures and Algorithms 32 (2008) 1–19 [7] Chung, F., Lu, L.: Connected...

Ngày tải lên: 08/08/2014, 01:20

... Z 4 and the complementary (36, 21, 12)-difference set. In the next section, we will reproduce the construction of the corresponding M and G given in [6] 3 (36, 15, 6)- and (36, 21, 12)-difference ... set M d of matrices of order 4 d+1 h 2 and a cyclic group G d of bijections M d →M d satisfying the following conditions: (a) M d contains the incidence matrix M d of a symmet...

Ngày tải lên: 07/08/2014, 06:22

... physicists in connection with Quantum Chaos. In particular, Haake and collaborators have computed the variance of the coefficients of these polynomials and raised the question of computing the higher ... (66) where Sc j (M)isthej-th secular coefficient. We are interested in moments of Sc j (M) with respect to µ N (M). The combinatorial significance of the higher moments of the...

Ngày tải lên: 07/08/2014, 08:22