Báo cáo toán học: " Graphs with Given Degree Sequence and Maximal Spectral Radius" doc

... of finding connected graphs of maximal spectral radius with given number of vertices and edges (but arbitrary degree sequences). Brualdi and Solheid [4] have shown that such graphs have stepwise ... of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequen...

Ngày tải lên: 07/08/2014, 21:20

... [6] showed that graphs with a hamiltonian path have no chromatic roots in (1, 1.29559 . . .). Both Jackson’s graphs with chromatic roots close to 32/27 and Thomassen’s graphs with chromatic roots ... v 4 } outside S and T . For example, Figure 2 represents colourings where three distinct colours a, b and c are used, v 0 , v 1 and v 3 are coloured a and v 2 and v 4 are...

Ngày tải lên: 07/08/2014, 13:21

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Ngày tải lên: 05/08/2014, 15:20

... obtained by replacing each vertex u ∈ V (H) with a set V u of size x u and each edge uv ∈ E(H) with a complete bipartite graph with vertex classes V u and V v . Theorem 1 Let 2 ≤ r ≤ n, (ln n) −1/r 2 ≤ ... simple. - Using random graphs, it is easy to see that most graphs on n vertices contain substantially many copies of any fixed graph, but contain no complete bipartite subgraphs...

Ngày tải lên: 07/08/2014, 15:23

... G 1 a×c and G 2 a×c by identifying v x,y with w x,y for all x and y such that x ∈ {0, a} or y ∈ {0, c}; and adding a n edge between v x,y and w x,y whenever 0 < x < a and 0 < y < c, and ... Chartrand, D. Erwin, G. L. Johns, and P. Zhang. Boundary vertices in graphs. Discrete Math., 263(1-3):25–34, 20 03. [3] G. Chartrand, D. Erwin, G. L. Johns, and P. Zhang. On...

Ngày tải lên: 08/08/2014, 12:23

... achieve the degree- maximal degree sequence d = (23, 19, 18, 17, 15, 12, 11, 7, 4). the electronic journal of combinatorics 15 (2008), #R14 12 Definition 2.7. (Degree- maximal families) Given two sequences ... {123, 124, 125}, with degree sequences (3, 2, 2, 1, 1) and (3, 3, 1, 1, 1). Clearly d(K  )  d(K), hence K is not degree- maximal. It is not hard to check that K  is...

Ngày tải lên: 07/08/2014, 15:23

... generalized Stirling numbers of the first and second kind S 1 (α, β, r)andS 2 (α, β, r) as introduced by Hsu and Shiue [17]. We show that in the case where β = 0and and r are nonnegative integers both ... when i =0andj =1,ourtypeI(p, q)-Stirling numbers of the first and second kind, s 0,1 n,k (p, q)andS 0,1 n,k (p, q), have been studied by a number of other authors, see [18], [19], [27]...

Ngày tải lên: 07/08/2014, 08:22

... a set with exactly two heavy vertices, then (3.16) and (3.17) yield that either F ′ contains three vertices of degree six and two vertices of degree five or four vertices of degree six and one of degree ... = 8 so either F ′ contains four vertices of degree eight and three vertices of degree four or five vertices of degree eight and two vertices whose degrees sum to fo...

Ngày tải lên: 08/08/2014, 14:22

... A. Gy´arf´as, and R.H. Schelp 1991a Odd cycles in graphs of given minimum degree. In: Y. Alavi, G. Chartrand, O.R. Oellermann, and A.J. Schenk, eds., Graph Theory, Combinatorics, and Applica- tions ... complete graph) and on even and odd polygons and paths in graphs and digraphs. Nevertheless, it was not always easy to decide what belongs. I have employed the following pr...

Ngày tải lên: 07/08/2014, 05:23

... two Latin subsquares, LB and LC have one Latin subsquare and LD has no Latin subsquares. Let GB and GC be the OQW graphs associated with LB and LC. GC has four vertices of degree six, 112, 130, ... Quistorff, and A. Wassermann. New results on codes with covering radius 1 and minimum distance 2. Designs, Codes and Cryptography, 35:241– 250, 2005. [10] J. Quistorff. On codes...

Ngày tải lên: 07/08/2014, 15:23