Báo cáo toán học: "The Strongly Regular (45, 12, 3, 3) Graphs" docx

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Ngày tải lên: 05/08/2014, 10:20

... class="bi x0 y0 w1 h 2" alt =""

Ngày tải lên: 05/08/2014, 15:21

... a strongly rpp semigroup. Again by Lemma 3.7 and the definition of a strongly right (left) adequate semigroup, we can formulate our main theorem. Theorem 3.8. (i) The translational hull of a strongly ... the translational hull of a strongly right (left) adequate semigroup is still the same type. Thus, the result obtained by Fountain and Lawson in...

Ngày tải lên: 06/08/2014, 05:20

... ,A k denote the bridges of the endpoints of e;thereare only finitely many of them, since G is locally finite. Then k ≥ 3 and one of the A i is the edge e itself. If A i consists of more than a single ... Invariance of T e Proposition 1 Let G be a locally finite 2-connected graph, and let e be an edge of G.IfT is any 3-block tree for G, then T = T e . Proof: We will show that th...

Ngày tải lên: 07/08/2014, 06:20

... the electronic journal of combinatorics 7 (2000), #R22 2 1 Introduction A strongly regular (40, 12, 2, 4) graph is a regular graph on 40 vertices of degree 12 such that each pair of adjacent ... non- adjacent neighbours has 4 common neighbours. In [3] an incomplete enumeration of strongly regular (40, 12, 2, 4) graphs established the existence of at least 27, a...

Ngày tải lên: 07/08/2014, 06:20

... point is a vertex. Such a drawing is said to be a rectilinear drawing of G.Therectilinear crossing number of G,denoted ν(G), is the fewest number of edge crossings attainable over all rectilinear ... rectilinear drawing of K n is a triangle. Prove that the convex hull of any optimal rectilinear drawing of K n is a triangle. 2. Given a rectilinear drawing...

Ngày tải lên: 07/08/2014, 06:22

... theorem. Theorem 1 The size of a minimum connected dominating set of a random n-vertex cubic graph is asymptotically almost surely less than 0.5854n. Proof After the first element of C has been chosen, ... least to within an additive constant, of the main result of [10]. They also showed that the size of a connected dominating set of an n-vertex cubic graph of gir...

Ngày tải lên: 07/08/2014, 06:23

... 1. ProofofTheorem3: Let a(G) be the number of automorphisms of an unlabeled n-vertex graph G. The number of distinct labelings of G is n!/a(G). If f (·)isa statistic on graphs, its expectation on labeled ... the proofofTheorem1. 1.9 1.92 1.94 1.96 1.98 2 2.02 2.04 0 0.2 0.4 0.6 0.8 1 t Figure 2: The plot of à (t) for 0 t ≤ 1. 4 Proof of Theorems 2 and 3 Proof of Theorem 2...

Ngày tải lên: 07/08/2014, 07:21

... that admits no cover pebbling, all pebbles may be concentrated to one of the fat nodes 1 with cover pebbling still not possible. Proof. Start with a distribution that admits no cover pebbling. If ... cover pebbling from f exceeds the total value of the pebbles. Therefore, cover pebbling is not possible with all pebbles initially on f .  4 The cover number for some classe...

Ngày tải lên: 07/08/2014, 08:22

... factor of 4 of the bound for the undirected case. We have now seen that the eigenvalues of the Laplacian can be used to control the diameter of the graph. It is also known that the eigenvalues of ... for the rate of convergence in terms of λ? Another important consequence of the Laplacian eigenvalues is its relationship with the Cheeger constant of a directed g...

Ngày tải lên: 07/08/2014, 13:21

... 7(1), (2000). [12] E. Spence, Strongly Regular Graphs,URL:http://www.maths.gla.ac.uk/~es/ srgraphs.html, (2004). the electronic journal of combina torics 13 (2006), #R32 9 (v, k, ,à) =(45, 12, 3, 3), providing ... at least n − 25. the electronic journal of combina torics 13 (2006), #R32 3 The Strongly Regular (45, 12, 3, 3) Graphs Kris Coolsaet, Jan Degraer Departm...

Ngày tải lên: 07/08/2014, 13:21

... square all-1 matrix. Proof of Theorem 1.1: The square of the number of perfect matchings of G counts ordered pairs of such matchings. We claim that this is the number of spanning 2-regular subgraphs ... Cuckler and J. Kahn, Entropy bounds for perfect matchings and Hamiltonian cycles, to appear. [3] S. Friedland, An upper bound for the number of perfect matching...

Ngày tải lên: 07/08/2014, 15:22

... is necessary for separability of density matrices of any graph and is sufficient for separability of density matrices of nearest point graphs and perfect the electronic journal of combinatorics ... recall the definition of the density matrices of a graph and define the tensor product of three graphs, reconsider the tripartite entanglement properties of the den...

Ngày tải lên: 07/08/2014, 15:22

... distance-regular if each vertex has at least one vertex at distance d and its distance-d adjacency matrix A d is a polynomial of degree d in the adjacency matrix A. This result is halfway towards the spectral ... distance-regular. This conclusion is the spectral excess theorem for this case. the electronic journal of combinatorics 15 (2008), #R129 4 The spectral excess...

Ngày tải lên: 07/08/2014, 21:20

... (2) Interestingly, the shifted hook length formula was discovered before the non- shifted one [Thr52]. Shortly after the fa mous G r eene-Nijenhuis-Wilf probabilistic proof of the ordinary hook length for ... 7, the hook length formula gives f 322 = 7! 5 · 4 · 1 · 3 · 2 · 2 · 1 = 21. 1 2 3 4 5 6 7 Figure 1: Young diagram [λ], λ = 66532, hook H 23 with hook length h 2...

Ngày tải lên: 08/08/2014, 14:23