Báo cáo toán học: "Distinguishing Cartesian Powers of Graph" ppsx

... Distinguishing Cartesian Powers of Graphs Michael O. Albertson Department of Mathematics Smith College, Northampton, MA 01063 USA albertson@math.smith.edu Submitted: ... id}.Callm(σ)themotion of σ and m(G)themotion of G. Using an appealing probabilistic argument Russell and Sundaram showed that if the motion of G is large, then the distinguishing number of G is small. ... x.An...

Ngày tải lên: 07/08/2014, 08:22

... c(b k−1 ) = ∆. Let S ⊆ V (G) consist of the union of all the vertices in levels 0 through k − 1 of T . Because of our choice of C and r, G[S] ∼ = T [S], with a ll leaves of G[S] at level k − 1. Since ... a perfect square, then the vertices of both X and Y consist of √ n subsets of √ n vertices (the vertices of subset 1 having subscripts 1 through √ n, those of subset 2 h...

Ngày tải lên: 07/08/2014, 21:21

... electronic journal of combinatorics 2 (1995) #R16 3 2Proofs 2.1 Proof of theorem 1 We need a few lemmas before proving theorem 1. Lemma 1 The inequality of theorem 1 holds when n ≤ 6. Proof of lemma 1: Done ... clutter. The shadow of a collection A of k -sets (set of size k ) is defined as the collection of the ( k − 1)-sets which are contained in at least one k -set of A. Th...

Ngày tải lên: 07/08/2014, 06:20

... v ν(Π,P,¯u, v), the number of Π-subposets of P containing v but not u ν(Π,P,u,¯v), the number of Π-subposets of P containing u but not v ν(Π,P,¯u, ¯v), the number of Π-subposets of P containing neither ... particular set of patterns rather than a singleton set. Let Π denote a set of patterns all of the same length k. For any permutation σ of length n let ν(Π,σ) be the numb...

Ngày tải lên: 07/08/2014, 06:23

... cycles of a graph G corresponds to a unique conjugacy class of the fundamental group π 1 (G, v) of G at a vertex v of G. The (Ihara) zeta function of a graph G is defined to be a function of u ∈ ... [10] showed that the zeta function of a regular covering of G is a product of L-functions of G. Stark and Terras [16] treated zeta functions of bipartite coverings of graphs...

Ngày tải lên: 07/08/2014, 13:21

... no vertex of T 0 is adjacent to any vertex of L. The distance of any vertex in T 0 from the farthest vertex in C is at most r + i/2. The distance of any vertex in the previous copies of T r p in ... journal of combinatorics 18 (2011), #P108 3 of degree one and let v be any such vertex of G. Set G ′ = G \ v. We may assume that H contains an induced copy of G ′ . Denote this c...

Ngày tải lên: 08/08/2014, 14:23

... variant of Vandermonde’s determinant. the electronic journal of combinatorics 11(2) (2005), #R19 10 From the computational point of view, with the help of Maple or other softwares, it is, of course, ... N 2 ). Recently, the problem of q-analogues of the sums of powers has attracted the attention of several authors [2, 9, 8], who found, in particular, q-analogues of the F...

Ngày tải lên: 07/08/2014, 08:22

... purposes of proving that the game coloring number of Cartesian products is not bounded by a function of game coloring numbers of factor graphs. However the class of Cartesian products of stars ... proof of this result more transparent, we introduce the so-called game of combinations which could also be of independent interest. At the end of this section we present some...

Ngày tải lên: 07/08/2014, 21:20

... skeleton of a structure A is the set of finite induced substructures of A and the age of A consists of all relational structures isomorphic to an element of the skeleton of the electronic journal of ... main of a function g, then g(B) means the setwise mapping of its elements {g(b) : b ∈ B}. The disti nguishing n umber of A, wr itten D(A), is the smallest cardinality of...

Ngày tải lên: 08/08/2014, 11:20

... conductivity values of BLTM were lower than those of undoped BLT ceramic regardless of measurement frequency. This seemed to be the effect of the donor dopant on the electrical conductivity of a p-type ... properties of (1 – x)PMN–xPZT ferroelectric ceramics. Phys Solid State 2000, 42:936-943. 21. Baudry L: Theoretical investigation of the influence of space charges on f...

Ngày tải lên: 20/06/2014, 20:20