Báo cáo toán học: "Nim-Regularity of Graphs" docx

... 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 ... non-complete graph of order 4. 1 Introduction Let G be a simple graph with vertex set V and edge set E. The number of vertices of a graph is its order.Thedegree of a vertex v...

Ngày tải lên: 07/08/2014, 13:21

... 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

... 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

... H. Proof . Let {e, f } be the pair of edges of G and let { u, v} be the pair of vertices of H that are involved in the dot product G · H. To prove (a) consider a pair {x, y} of edges of G neither of ... froof of (b), let a i (i = 1, 2, 3, 4) denote the edge of G · H obtained by the junction of the i-th semiedge of G L with that of H R . Furthermore let u and v be the e...

Ngày tải lên: 08/08/2014, 12:22

... repeat of u (and vice versa) in G. Clearly, when defect is 2, R(G) is either one cycle of length n = |V (G)| or a disjoint union of cycles whose sum of lengths is equal to n. If R(G) is cycle of ... 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...

Ngày tải lên: 08/08/2014, 14:22

... context of line graphs, an ordinary graph is effectively all negative. The line graph of a bidirected all-positive graph—that is, of a directed graph— is the full notion of line graph of a digraph, of ... even number of triples in the class. Equivalent to a Seidel switching class of simple graphs. (The triples are the ones supporting an even number of edges of the graph; th...

Ngày tải lên: 07/08/2014, 05:23

... action of A 7 on S a little further, considering orbits of pairs of triples of elements of S (which correspond to edges or non-edges in L 2 ). One counts 70 pairs of disjoint triples, 315 pairs of ... must correspond to a union of orbits of A 7 on pairs of triples from S,sinceA 7 acts as a group of automorphisms of L 2 ). We anticipate Lemma 43 which identifies L 2 with...

Ngày tải lên: 07/08/2014, 08:22

... symmetry of solutions of (1.1) on the hyperbola (1.3). For ξ = η = 0 and max{1, 2/(N − 2)} < p, q < ∞, Chen and Li [16, Theorem 4.3] obtained the nonexistence of positive solutions of (1.1) ... some assumptions of p, q, α, and β. Furthermore, using Doubling Lemma indicated in [14], which is an extension of an idea of Hu [15], Chen and Li [16, Theorem 4.3] obtained the none...

Ngày tải lên: 20/06/2014, 21:20

... ∂Ω. Therefore, the problem admits only the null solution. Proof Similar to the proof of theorem 1. theorem 3.3 If u k ∈ W 1,p k (x) 0 (Ω) ∩L ∞  Ω  solution of the system (1.6) −(1.7), Ω is a star shaped ... identities (2.5) and (2.6). The rest of the proof is similar to the that of lemma 1. 3 Principal Result theorem 3.1 If u ∈ W 1,p(x) 0 (Ω) ∩ L ∞  Ω  be a solution of the probl...

Ngày tải lên: 20/06/2014, 21:20

... possibility of underestimation of PFC exposure through food contact materials. Mixtures of perfluorooctanesulfonamide esters are often used in the manufacture of water- and greaseproof papers ... eating 8 g of eel from Belgium with a concentration of 857 µg PFOS/kg fresh weight or eating 0.6 g of trout from the upper Sauerland region of Germany with a measured maximum leve...

Ngày tải lên: 20/06/2014, 21:20