Báo cáo toán học: "Extension of Strongly Regular Graphs" potx

... ∩ N(v)| to denote the number of neighbors of u (the degree of u) and the number of common neighbors of u and v, respectively. An n-vertex graph is called strongly regular, denoted SRG(n, r, λ, ... Characterization of Irregular (λ, µ)-graphs In this section we prove that K 1 ∨ mK λ+1 is the only type of connected irregular (λ, µ)- graphs. A nice interpretation of the result...

Ngày tải lên: 07/08/2014, 15:23

... matchings in  -regular graphs Noga Alon ∗ School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540 and Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel ... The solution of the van der Waerden problem for permanents, Dokl. Akad. Nauk SSSR 258 (1981), 1041-1044. [4] D. I. Falikman, A proof of van der Waerden’s conjecture on the pe...

Ngày tải lên: 07/08/2014, 06:22

... generalization of bo th distance-regularity and walk-regularity, which we call k-walk-regularity. In particular, we present some algebraic characterizations of k-walk -regular graphs in terms of the so-called local ... a (ℓ) uv is independent of u, v, provided that dist(u, v) = i ≤ k, and G is k-walk -regular. Conversely, suppose that G is k-walk -regular and consider the set of n...

Ngày tải lên: 07/08/2014, 21:21

... monotonicity of f(δ) in the required range, and completes the proof of the theorem. ✷ References [1] A. Alon, S. Hoory, N. Linial, A Continuous Analogue of the Girth Problem, Journal of Combinatorial ... electronic journal of combinatorics 14 (2007), #N1 4 Maximum matchings in regular graphs of high girth Abraham D. Flaxman Microsoft Research Redmond, Washington, USA abie@micros...

Ngày tải lên: 07/08/2014, 13:21

... number of reaches of G M equals the algebraic and geometric multiplicity of 0 as an eigenvalue of M. Proof. Let R 1 , , R k denote the reaches of G M and let H i denote the exclusive part of R i for ... 3 Proof. Let M = D − DS be given as stated. As in the proof of Theorem 3.2 above, we may assume without loss of generality that S ii = 1 whenever D ii =0. (2) We further observ...

Ngày tải lên: 07/08/2014, 13:21

... journal of combinatorics 15 (2008), #R134 15 irreducible rank 4 (2, 3)-graphs without proof in proposition 79. There are four of them, two of which are Coxeter and two of them are not. Both of the ... our proof of (72) and thereby (71). Of course, θ u is the inverse of the restriction F 0 : R I (u, −) → K n of the functor F . We define a left K n -action on R I (u, −), the ve...

Ngày tải lên: 07/08/2014, 21:21

... a proof of which is elementary and is omitted. Lemma 4.8 If S is an independent set of a path P , consisting of internal vertices of P , then |N P (S)| ≥ |S| + 1. the electronic journal of combinatorics ... achment in C, i.e., A = N C (H 1 ). Let U be the set of successors of vertices of A on C, and let W be the set of predecessors of vertices of A on C. We first note tha...

Ngày tải lên: 08/08/2014, 14:22

... question of whether or not the procedure distinguishes all strongly regular graphs is still open. The quantum walk procedure of Douglas and Wang in [1] has also been t ested on classes of strongly regular ... regular graphs and of regular g raphs, where all non-isomorphic graphs were distinguished. Finding a pair of non-isomorphic strongly regular graphs which are no...

Ngày tải lên: 08/08/2014, 14:23

... journal of combinatorics 10 (2003), #R11 10 Proof: Let S = {x 1 ,x 2 , ··· ,x k } be an ordered subset of the vertices of G.LetC be a cycle of maximum order 2c containing all vertices of S in ... contradiction to the above inequality. Let c be the number of elements of S that are not vertices on any of the k + t edges of the matching. Then t + d + c of the edges are free....

Ngày tải lên: 07/08/2014, 07:21

... graph Γ of a strongly regular graph Γ with parameters (v, k, λ, µ) is a strongly regular graph with parameters (v, v − k − 1,v− 2k + µ −2,v− 2k + λ). The adjacency matrix A of a strongly regular ... switching of edges in graphs is the fact that if certain conditions are satisfied then switching of edges in a strongly regular graph may produce another strongly regular...

Ngày tải lên: 07/08/2014, 07:21