Báo cáo toán học: "Edge-magic group labellings of countable graphs" ppsx

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Ngày tải lên: 05/08/2014, 09:46

... class="bi x0 y0 w1 h 1" alt =""

Ngày tải lên: 05/08/2014, 10:20

... Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd girth, The Electronic Journal of Combinatorics 1 (1994) #R9. 2 We can now prove the following theorem. Theorem ... is sharp for the regular complete bipartite graphs K aa . The above results are readily extended to graphs of larger odd girth. Lemma 2: Let G have odd girth...

Ngày tải lên: 07/08/2014, 06:20

... chordless. The length |C| of a cycle C is the number of its edges. The length (B) of a cycle basis B is sum of the lengths of its cycles: (B)=  C∈B |C|.Aminimal cycle basis is a cycle basis with minimal ... . 5. Minimal Cycle Bases of Outerplanar Graphs Let (G, V ) be a 2-connected outerplanar graph. The set T = H \{(1,n)} is a spanning tree of G(V,E). The fun...

Ngày tải lên: 07/08/2014, 06:22

... tight. The odd edge-connectivity of a graph G is the size of a smallest odd edge cut of G.The odd girth of G is the length of a shortest odd cycle of G. Zhang [19] proposed a strengthing of Jaeger’s ... of length at least 2k. For otherwise, for any internal vertex x of a thread of length the electronic journal of combinatorics 8 (2001), #R25 3 Circular chromati...

Ngày tải lên: 07/08/2014, 06:22

... 05C83 Abstract The arc-representation of a graph is a mapping from the set of vertices to the arcs of a circle such that adjacent vertices are mapped to intersecting arcs. The width ofsucharepresentationisthemaximumnumberofarcshavingapointincommon. The ... width ofsucharepresentationisthemaximumnumberofarcshavingapointincommon. The arc-width( aw) of a graph is the minimum wid...

Ngày tải lên: 07/08/2014, 06:22

... a little bit of new machinery. An often studied subset of graceful labellings are bipartite graceful (or α -graceful) labellings; the labelling f of G is bipartite if the vertices of G have a bipartition ... variations of gracefulness which relax distinctness conditions (such as equitable labellings) introduce new constraints as well. While in a sense vertex-relaxed gracefu...

Ngày tải lên: 07/08/2014, 06:23

... inequalities are the numbers v k of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers d k and v k for k<50 and prove the following exponential bounds: 1.67 k <v k < ... lattices, one rather considers the vertical sum in that case, where the only difference to the former is that now the top element  1 of...

Ngày tải lên: 07/08/2014, 06:23

... the set of labels of the Vertices of H. ã H E denotes the set of labels of the Edges of H. ã B E denotes the set of labels of the Edges Between H and I. ã I V denotes the set of labels of the ... small modification of the proof is required for any countable subgroup of real numbers which does not include 2. For let g be an element of the group such that g ≥ 2. In...

Ngày tải lên: 07/08/2014, 13:21

... referee for the useful remarks. the electronic journal of combinatorics 14 (2007), #N21 6 Regular spanning subgraphs of bipartite graphs of high minimum degree B´ela Csaba ∗† Submitted: Aug 1, 2007; ... electronic journal of combinatorics 14 (2007), #N21 2 3.2 Proof of part II For proving part II of the theorem we want to construct a class of balanced bipartite...

Ngày tải lên: 07/08/2014, 15:22

... applicable. These methods provide product formulas for a large class of Hankel determinants. A modern treatment of the theory of determinant evaluation including Hankel determinants as well as a ... further difficulties that arise in the consideration of other (β, α)-cases in Section 7. A number of additional almost product evaluations of Hankel determinants are given in...

Ngày tải lên: 07/08/2014, 15:22

... a perfectly balanced partition almost surely. Smoothed Graphs. Smoothed analysis studies the behavior of objects after adding a small amount of randomness. This concept was introduced in the context of ... journal of combinatorics 16 (2009), #N14 6 • ∆(G) − δ(G) ≤ 2αn. • G has a degree matching of size at least 2αn. In the course of the proof of Lemma 5, we need the follo...

Ngày tải lên: 07/08/2014, 21:21

... proof of Theorem 1, and discussed three different zeta functions of any graph. Various proofs of Bass’ theorem were known. Kotani and Sunada [15] proved Bass’ theorem by using the property of ... Ihara zeta function of a fractal graph, and gave a determinant expression of it. We define the Bartholdi zeta function of a fractal graph, and present its determinant expressi...

Ngày tải lên: 07/08/2014, 21:21

... distinguishing chromatic number of K n,n − M We denote by K n,n − M the graph obtained from the complete bipartite graph K n,n by deleting the edges of a perfect matching. This graph arises in the proof of ... 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 le...

Ngày tải lên: 07/08/2014, 21:21

... graphs with maximum Laplacian spread among all tricyclic gr aphs of order n ≥ 11. Moreover, fo r 5 ≤ n ≤ 10, if G is one with maximum Laplacian spread of all tricyclic gra phs of order n, then G ... vertices of the star, respectively [4]. A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. In this paper, we stud...

Ngày tải lên: 07/08/2014, 21:21