Báo cáo toán học: "The maximum distinguishing number of a group" ppt

... permutation of X. In this paper, we show that if G is nilpotent of class c or supersolvable of length c then G always acts with distinguishing number at most c + 1. We obtain that all metacyclic ... groups act with distinguishing number at most 3; these include all groups of squarefree order. We also prove that the distinguishing number of the action of the general lin...

Ngày tải lên: 07/08/2014, 13:21

... dense random graph. The notion of a t-stable set is a generalisation of the notion of a stable set. Recall that a set of vertices S of a graph G is stable if no two of its vertices are adjacent. ... (B) We treat this case similarly. We consider an auxiliary bipartite graph as above. Let c ∈ S 2m (t, k) be a configuration of balls 1, . . . , 2m. Since there are at most...

Ngày tải lên: 08/08/2014, 12:22

... optimal rectilinear drawing of K n is a triangle. 2. Given a rectilinear drawing of G,theplanar subdivision of G is the graph obtained by adding vertices (and corresponding adjacencies) at each of ... crossings in a nested triangle drawing of K 9 is at least nine. Proof: We make use of the fact that the green and blue triangles form a K 6 and that any rectilinear drawing...

Ngày tải lên: 07/08/2014, 06:22

... Information Science University of Ljubljana Ljubljana, Slovenia gasper.fijavz@fri.uni-lj.si David R. Wood ∗ Departament de Matem´atica Aplicada II Universitat Polit`ecnica de Catalunya Barcelona, ... Number of Graphs with an Excluded Minor Drago Bokal Department of Combinatorics and Optimization University of Waterloo Waterloo, Canada dbokal@uwaterloo.ca Gaˇsper Fijavˇz Faculty of...

Ngày tải lên: 07/08/2014, 15:22

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Ngày tải lên: 05/08/2014, 10:20

... 2n+1ofthen eigenvalues of R are equal to 1, and also that there is an eigenvalue x n ∼ √ n. Jarvis [6] proved that there is a real negative eigenvalue ∼− √ n, and that the other eigenvalues cannot ... theoretic way, recall that an ordered factorization of an integer m is a representation m = a 1 a 2 a k ,inwhichalla i sare≥ 2 and the order of the factors is important. Now in...

Ngày tải lên: 07/08/2014, 08:22

... rows and columns of the adjacency matrix of G it is a block diagonal matrix in which every block is an all-1 square matrix, and as our graph G has no loops, this means that it is a union of complete ... a square all-1 matrix. Proof of Theorem 1.1: The square of the number of perfect matchings of G counts ordered pairs of such matchings. We claim that this is the numbe...

Ngày tải lên: 07/08/2014, 15:22

... and radius 2, with endpoints b, c and central angle π 3 . Similarly arcs A b and A c are defined. In other words, the points a, b, c and the arcs A a , A b , A c form the vertices and edges of a ... We define an upper boundary of D as an arc, which is a common boundary of D and D (in case that a 1 = l 1 we define the upper boundary as {l 1 }). Similarly we define a lower...

Ngày tải lên: 07/08/2014, 15:23

... the size of a partial spread in such a space, an intriguing question. A partial spread is said to be maximal if it cannot be extended to a larger partial spread. In [1], partial spreads of size ... tight and is a generalisation of the result of De Beule and Metsch for the case ρ = 2. 1 Introduction A partial spread of a polar space is a set of pairwise disjoint gen...

Ngày tải lên: 07/08/2014, 21:21

... even. This paper makes a natural generalization from these two results. Namely, it finds an expression for the maximum CR(R n,d ) of all maximum rectilinear crossing numbers for the class R n,d of all ... order of a graph G is defined as the cardinality of V (G). A drawing of the graph G is a representation of G in the plane such that the elements of V (G) correspond t...

Ngày tải lên: 07/08/2014, 21:21