Báo cáo toán học: "Compositions of Graphs Revisited" pptx

... V (G). A composition of G is a partition of V (G) into vertex sets of connected induced subgraphs of G. Thus a composition provides a set of connected induced subgraphs of G, {G 1 , G 2 , · · ... composition of a graph G is a partition of the vertex set of G into vertex sets of connected induced subgraphs of G. Knopfmacher and Mays [2] found an explicit formula for C(K m...

Ngày tải lên: 07/08/2014, 13:21

... the set of n n functions from [n]to[n]. Let A n be the n element subset of U n consisting of the constant functions: g ∈ A n iff g(i)=g(j) for all i, j.Let f 1 ,f 2 ,f 3 , be a sequence of random ... by striking out the first row and column of P .ThenE(T ) is exactly the sum of the entries in the last row of (I − Q) −1 . See, for example, chapter 3 of [5]. This fact is very conv...

Ngày tải lên: 07/08/2014, 06:23

... of G is a set of subgraphs G 1 , ,G t such that any edge of G is an edge of exactly one of G 1 , ,G t and all G 1 , ,G t ∈ .Letφ(G, ) denote the minimum size of an -decomposition of G. The main ... result on decompositions of graphs into connected non- bipartite non-complete graphs of order 4 and single edges. Let H be one of the following graphs. Theorem 2.4. Any gr...

Ngày tải lên: 07/08/2014, 13:21

... bijection between the set of vertices of G and the set of vertices of H. We now show that given any pair a, b of vertices of G (which might also coincide), the set E(a, b) of edges between these ... journal of combinatorics 16 (2009), #N6 1 of f(a) and thus the 3ε-neighborhood of f (a) is a simple arc (lying in the interior of some edge) in H. Consider the points a 1 , a...

Ngày tải lên: 07/08/2014, 21:21

... electronic journal of combinatorics 18 (2011), #P71 4 Nonexistence of graphs with cyclic defect Mirka Miller ∗† School of Electrical Engineering and Comp. Science, University of Newcastle, Australia Department ... consider graphs of maximum degree ∆, diameter D and order M(∆, D) − 2, where M(∆, D) is the Moore bound, that is, graphs of defect 2. In [1] Delorme and Pineda-Vil...

Ngày tải lên: 08/08/2014, 14:22

... interrelations of mathematics, geometry and art. The conference resulted in a friendship and an exchange of letters. One of these letters of Coxeter to Escher contained a rendering of a hyperbolic ... rotated version. From the position of a peak, the location of the possible center(s) of rotatio n or axis of translation can be derived. Also the glide distance of a glide re...

Ngày tải lên: 08/08/2014, 01:20

... in terms of random embeddings of pairs of graphs in K n . Theorem 1, discusses random embeddings of t-tuples of graphs. In Theorem 2, we use this to extend Tomescu’s result from graphs of bounded ... the proof, we speak of the probability of various events, and evaluate the expected value of some random variables. The underlying probability space for all this is the set...

Ngày tải lên: 07/08/2014, 06:20

... application of the ↔-partition of R we derive bounds on the number of distinct minimal cycle bases of G. the electronic journal of combinatorics 7 (2000), #R16 10 ordering of the vertex set V of G.SetV r = ... C. The set C of all generalized cycles forms a subspace of (E, ⊕, ·) which is called the cycle space of G.AbasisB of the cycle space C is called a cycle basis of...

Ngày tải lên: 07/08/2014, 06:20

... W of indices write A W for the submatrix of A consisting of all rows and columns index with elements of W . It is easy to see by inspection that each of the blocks Adj(A) γ i (a) is of one of ... class of τ 0,γ is an orbit of g d/d  1 . Hence the equivalence classes of τ 0,γ are the orbits of g d/d  1 , and, therefore, they are orbits of g d/d  . Thus, each eq...

Ngày tải lên: 07/08/2014, 06:22