Báo cáo toán học: "Spectral characterizations of dumbbell graphs" docx

... spectrum of D a,b,0 (with δ  3). Lemma 3.4. The spectrum of D a,b,0 with δ = gcd(a, b)  3 consists of the eigenvalues of C δ (except 2 and −2) with multiplicity 3, the eigenvalues of C a and ... eigenvalues of C a ∪ C b and be of multiplicity 1. This ends the proof. From the above lemma we know to some extent the spectrum of D a,b,0 . If H is a tentative cospectral mate of...

Ngày tải lên: 08/08/2014, 12:22

... member of the second coordinate of the label of y, delete the edge x j y.If the digit of z is 3 and y is not a member of the second coordinate of the label of z, delete the electronic journal of ... Subclaims, the proof of our lemma is complete. 5 Proof of the Main Theorem In this section, we present the proof of the main theorem. Let C be a topologically closed class o...

Ngày tải lên: 07/08/2014, 06:23

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 09:46

... Subsquares of N 2 squares of order 9. In particular we note that there are 1589 main classes of N ∞ squares of order 9, yet only 37 of these contain pan-Hamiltonian squares. In terms of reduced ... have a generalisation of Lemma 4. §6. Small orders For n ∈{2, 3, 5} thecatalogueofLatinsquaresin[5]showsthatthereisasinglemain class of N ∞ square of order n,namelythatofC n . Acc...

Ngày tải lên: 07/08/2014, 06:20

... result of Kannan, Tetali and Vempala to com- pletely solve, via a simple proof, the problem of random generation of a labeled tournament with a given score vector. The proof uses the method of path ... score vector of a tournament is the sequence of out- degrees of the vertices of the tournament. In general, given a score vector with n scores, there can be an exponential (in n...

Ngày tải lên: 07/08/2014, 06:20

... ordering of the vertices to an ordering of the edges lexicographically. A broken circuit of H ⊆ G is a set of edges B ⊆ H such that there is some edge e ∈ G, smaller than every edge of B, such ... consists of all edges of G with both ends in S. We will use the symbols π and σ to denote set partitions. The notation π  S means π is a set partition of the set S. The length (numb...

Ngày tải lên: 07/08/2014, 08:22

... one-factorization of type 4 + 4 + 4 is only possible for three graphs of order 12: the disjoint union of three copies of C 4 , the disjoint union of three copies of K 4 ,and the union of K 4 and the ... properties of the classified one-factorizations are also tabulated. 1 Introduction An r-factor of a graph G is an r-regular spanning subgraph of G.Anr-factorization of G i...

Ngày tải lên: 07/08/2014, 08:22