Báo cáo toán học: "The Strongly Regular (40, 12, 2, 4) Graphs" ppsx

... 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

... Spence, The Strongly Regular (40, 12, 2, 4) Graphs, Elec. Journ. Combin. 7(1), (2000). [12] E. Spence, Strongly Regular Graphs,URL:http://www.maths.gla.ac.uk/~es/ srgraphs.html, (20 04). the electronic ... multiplicity 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 Dep...

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 05/08/2014, 15:21

... 10 References [1] W. H. Cunningham and J. Edmonds, A combinatorial decomposition theory, Canad. J. Math. 32, 1980, 734–765. [2] C.Droms.B.ServatiusandH.Servatius,Connectivity of Groups, preprint [3] C.Droms.B.ServatiusandH.Servatius,Planar ... E. Hopcroft and R. E. Tarjan, Dividing a graph into triconnected components, SIAM J. Comput. 3, 2, 135–158, 1973. [5] D. J. Kleitman, Methods of inv...

Ngày tải lên: 07/08/2014, 06:20

... directed path from u to v.A directed graph is strongly connected if for any two vertices u and v, there is a directed path from u to v. The diameter of a strongly connected directed graph is defined ... bound the diameter using the eigenvalues. In this note we give a similar result for the diameter of strongly connected directed graphs G,namely D(G) ≤  2min x log(1/φ(x)) log 2 2−λ  +1...

Ngày tải lên: 07/08/2014, 13:21

... matchings of G counts ordered pairs of such matchings. We claim that this is the number of spanning 2 -regular subgraphs H of G consisting of even cycles (including cycles of length 2 which are the same ... with more than 2 vertices. Indeed, every union of a pair of perfect matchings M 1 , M 2 is a 2 -regular spanning subgraph H as above, and for every cycle of length exceeding 2 in H there...

Ngày tải lên: 07/08/2014, 15:22

... obtain Corollary 3. For n ≥ 0, T n (2, −1) = a n+1 and  n≥0 T n (2, −1) t n n! = sec(t)(tan(t) + sec(t)). the electronic journal of combinatorics 15 (2008), #N28 3 Theorem 1. T (K n ; 2, −1) = T (K n+2 ; 1, ... we obtain  n≥1 J n (−1)(−2) n t n n! = (−2) ln | cos(t) + sin(t)|. (4) Now, by differentiating twice both sides of equation (4) we conclude that  n≥0 J n+2 (−1)(−2) n t n n!...

Ngày tải lên: 07/08/2014, 15:22

... 1, 2, ··· , n} = {|u i ⊗ |v j ⊗ |w k  : i = 1, 2, ··· , m; j = 1, 2, ··· , p; k = 1, 2, ··· , q}, where {|u i  : i = 1, 2, ··· , m} is an orthonormal basis of C m A , {|v j  : j = 1, 2, ... orthonormal basis of C p B and {|w k  : i = 1, 2, ··· , q} is an orthonormal basis of C q C . Let i, r ∈ {1, 2, ··· , m}, j, s ∈ {1, 2, ··· , p}, k, t ∈ {1, 2, ··· , q}, λ ijk, rs...

Ngày tải lên: 07/08/2014, 15:22

... colouring of G − {u, v, w}. The elements vx, ux, uy, wy, u, uw, uv (1) have usable lists of at least 2, 2, 2, 2, 3, 5 and 5 colours, respectively, since ∆ + 1  5. (The vertices v and w can be coloured ... K 4 -minor-free and K 2,3 -minor-free. By a near-outerplanar graph we mean one that is either K 4 -minor- free or K 2,3 -minor-free. In fact, in the following theorem we will replac...

Ngày tải lên: 07/08/2014, 13:21

... Suppose k ≡ 3 (mod 4). Let k = 4ℓ + 3 and define the (4ℓ + 3)-cycles C and D on 2K 4ℓ+4 by C =(0, 1, 4ℓ + 2, 2, 4ℓ + 1, . . . , 3ℓ + 3, ℓ + 1, 3ℓ + 1, ℓ + 2, 3ℓ, . . . , 2ℓ, 2ℓ + 2, 2ℓ + 1, ∞); and D ... Suppose k ≡ 1 (mod 4). Let k = 4ℓ + 1 and define the (4ℓ + 1)-cycles C and D on 2K 4ℓ+2 by C = (0, 1, 4ℓ, 2, 4ℓ − 1, . . . , ℓ , 3 ℓ + 1 , ℓ + 2, 3ℓ, ℓ + 3, . . . , 2ℓ, 2ℓ + 2, 2ℓ...

Ngày tải lên: 08/08/2014, 01:20