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

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 3 C 2 C 1By Theorem 1, H ... Then for i =1, ,8, let C i= c i c ti, and letH = 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 3 C 2 C 1By ... 11−= c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 the electronic journal of combinatorics 8 (2001), #R1 3 Hadamard matrices and strongly regular graphs with the 3-e. c. adjacency propertyAnthony...

Báo cáo toán học: "An Inﬁnite Family of Graphs with the Same Ihara Zeta Function" potx

... impose an equivalence relation on two circuits c and c ′via cyclicpermutation.Remark 1. The distinction between cycles and circuits (circuits are cycles which do nothave backtracking or tails) ... vertices and by Zl the compo nent with 2 vertices.Similarly, upon removal of the bridge edge fn−2in the graph Ln, we are left with twoconnected components. We denote by Ln the component with ... n = 4, the graphs R4 and L4are isomorphic. Cooper conﬁrmed Theorem 6 forn = 5, . . . , 12 through direct computation of the zeta functions. In the next section, weprove t hat the theorem...

Báo cáo toán học: "Positive matrices and dimension groups affiliated to C*-algebras and topological Markov chains " docx

... h 3" alt ="" ...

Báo cáo toán học: "Venn Diagrams and Symmetric Chain Decompositions in the Boolean Lattice" ppt

... whenever C C and C is not a root chain, then there exists a chain π (C) ∈Csuch thatstarter (C) coversanelementπs (C) ofπ (C )and terminator (C) is covered by an element πt (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 longestchains in C the root chains.SaythatC has the chain cover property ... the chain cover graph, G (C, π), whose vertices are the elements of A and whose edges consist of the covering edges in the chains in C together with the cover edges, for each non-root chain C C, from:•...

Báo cáo toán học: "Sequentially perfect and uniform one-factorizations of the complete graph" pot

... order the 2n − 1one-factors of a one-factorization of the complete graph K2nin 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 6Acknowledgements The authors would like to to thank Dan Archdeacon, Cameron ... 7, 2005Mathematics Subject Classiﬁcations: 0 5C7 0AbstractIn this paper, we consider a weakening of the deﬁnitions of uniform and perfectone-factorizations of the complete graph. Basically, we...

Báo cáo toán học: " Independence number and disjoint theta graphs" doc

... so we need not consider the casewhere 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 froma triangle and two copies of C 4because the independence number of that graph is 5 ,a contradiction. Let C ... since G is K−4-free, aicannot beadjacent to 3 consecutive vertices of C. The remainder of the proof of this case consists of considering cases based on the structure of C .First suppose C...

Báo cáo toán học: "Short cycles in random regular graphs" pps

... C 2, C 3as follows:• (C 1 ,C 2) C 1if and only if C 2∩ C 1= ∅,• (C 1 ,C 2) C 2if and only if C 2∩ C 1= ∅ and C 2= C 1,• (C 1 ,C 2) C 3if and only if C 2= C 1.Note that Theorem ... Letting C denote the collection ofall r-cycles in Kn(considered as sets of edges),E(X2r)= C 1 C  C 2 C P (C 1 C 2⊆ G). (2.3)Partition the pairs (C 1 ,C 2) into three classes C 1, C 2, ... C 1 and C 2to have possibly diﬀerent lengths, r and s respectively, with r ∈ C and 3 ≤ s ≤ g. Classify the graphs H = C 1∪ C 2according to the number ofcomponents p and edges j in the intersection...

Báo cáo toán học: "he spectral gap of random graphs with given expected degrees" pot

... at the input.Therefore, the following procedure LowDisc basically tries all possible values for¯dmin 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 components in random ... these algorithms rely on the spectrum of the adjacency matrix, which is quite susceptible to ﬂuctuations of the vertex degrees. In fact, as Mihail and Papadimitriou [21] pointed out, in the case...

Báo cáo toán học: "New symmetric designs from regular Hadamard matrices" pdf

... Z4 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 Mdof matrices of order 4d+1h2 and a cyclic group Gdof bijections Md→Mdsatisfying the following conditions:(a) Mdcontains the incidence matrix Mdof a symmetric design with parameters(4d+1h2, ... is such a matrix, then the Kronecker product of a regular Hadamard matrix of order 4 and H is a regular Hadamard matrix of order 9 · 4d+1. Therefore, one can obtain a family of regular Hadamard...

Báo cáo toán học: "Random Matrices, Magic Squares and Matching Polynomia" ppt

... physicists in connection with Quantum Chaos. Inparticular, Haake and collaborators have computed the variance of the coeﬃcientsof these polynomials and raised the question of computing the higher ... (66)where Scj(M)isthej-th secular coeﬃcient. We are interested in moments of Scj(M) with respect to µN(M). The combinatorial signiﬁcance of the higher moments of the ﬁrst secular coeﬃcientSc1(M), ... zeta function on the critical line werecomputed and the following result was proved. the electronic journal of combinatorics 11(2) (2004), #R2 8Random Matrices, Magic Squares and MatchingPolynomialsPersi...

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