Báo cáo toán học: "he spectral radius of subgraphs of regular graphs" ppt

... [2] and its proof is omitted. Proofs Proof of Theorem 2 Write dist F (s, t) for the length of a shortest path joining two vertices s and t in a graph F. Write d for the degree of G, let H = G ... 184, Springer- Verlag, New York (1998), xiv+394 pp. [2] S. M. Cioab˘a, The spectral radius and the maximum degree of irregular graphs, Elec- tronic J. Combin., 14 (2007), R38. [3] V. Niki...

Ngày tải lên: 07/08/2014, 13:21

... distance -regular graphs. The usefulness of the spectral excess theorem is for example demonstrated in the re- cent discovery of a new family of distance -regular graphs with the same parameters of particular ... number of vertices at extremal distance proves the distance-regularity. The goal of this paper is to give an elementary and global proof of the spectral excess th...

Ngày tải lên: 07/08/2014, 21:20

... order Reed-Muller code, consisting of the sup- ports of all functions V → GF(2) of degree at most k. A Kerdock set K induces a Kerdock code consisting of the cosets of the RM 1 represented by the ... bent. the electronic journal of combinatorics 5 (1998), #R34 5 Thus we call a set of functions a bent Kerdock set if the sum of every two of them is bent. As before without loss...

Ngày tải lên: 07/08/2014, 06:22

... improve some recent results of Nikiforov [16] regarding the spectral radius of a subgraph of a regular graph. We also investigate the spectral radius of a graph obtained from a regular graph by adding an ... the spectral radius of a general (not necessarily regular) graph G and that of a subgraph of G, see [16]. 2 The spectral radius and the maximum degree...

Ngày tải lên: 07/08/2014, 15:22

... Proofs of Auxiliary Lemmas 7.1 Proof of Lemma 2.2 The proof of Lemma 2.2 relies on the following general tail bound, which is a consequence of Azuma’s inequality (cf. [17, p. 38] for a proof). Lemma ... 3. The proof of Proposition 1.1 shows that the basic reason why the spectral gap of a sparse random graph G(n, d) is small actually is the existence of vertices of degree ≪ ¯...

Ngày tải lên: 08/08/2014, 01:20

Ngày tải lên: 05/08/2014, 15:21

... ∅,B 2 (H t ) = ∅ and B 1 (H t ) = ∅. The proof of Lemma 4 is complete.  ProofofTheorem9. (a) Let k = 4. Then the graph L = S(I(L) ∪ K(L),E(L)) of Lemma 2 is a maximal nonhamiltonian Burkard–Hammer ... V (G), the set of all neighbors of W is denoted by N G (W )orN (W )inshort. Fora vertex v ∈ V (G), the degree of v, denoted by deg(v), is the number |N(v)|.The minimum degree of G...

Ngày tải lên: 06/08/2014, 05:20

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20