Báo cáo toán học: "Graphs Associated with Codes of Covering Radius 1 and Minimum Distance 2" ppsx

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Ngày tải lên: 05/08/2014, 10:20

... appear. [2]G.D.Cohen,I.Honkala,S.LitsynandA.Lobstein:Covering Codes, Elsevier, 1997. [3] M.G.Karpovsky,K.ChakrabartyandL.B.Levitin: Onanewclassofcodes for identifying vertices in graphs, IEEE Trans. Inform. Th., vol. 44, ... vertex of degree zero. Since, by symmetry, one element in C  2 produces two vertices with degree zero or New Bounds for Codes Identifying Vertices...

Ngày tải lên: 07/08/2014, 06:20

... shows that Construction 2 generates many non-isomorphic graphs. We then show that most of the graphs generated have the n-e.c. property in Section 4, thereby completing the proof of Theorem 1.1. The ... proof of the n-e.c. property uses bounds on the expected number of pairs of subsets U, W causing the graph not to be n-e.c. 2 Background The n-e.c. prope...

Ngày tải lên: 07/08/2014, 06:23

... 8 Constant- weight codes correspond to the partition {0, ,q− 1} = {0}∪{1, ,q− 1}, and constant- composition codes to the partition {0, ,q− 1} = {0}∪···∪{q − 1}.Our bounds for DNA codes with constant ... codewords with exactly w occurrences of two fixed characters. In this section we give lower bounds for DNA codes that are constructed from bi- nary codes, binary cons...

Ngày tải lên: 07/08/2014, 07:21

... the proof of Lemma 2 in our proof of Theorem 1, we will include the full proof of Lemma 2 there. As examples of these lemmas, for the symmetric group, which has m = n(n − 1)/2 roots, the asymptotic ... covariance form of X.LetY N be the sum of N independent copies of X. For any vector v,letp(v) be the probability for the random walk, and let q(v) the...

Ngày tải lên: 07/08/2014, 08:22

... continuity that the chromatic polynomial has a root in the interval (1, 2). We can perform a similar analysis on the graphs obtained by adding the single edge v 1 v 4 to X(s, t) with the following ... an in nite family of 3-connected non-bipartite graphs with chromatic roots in the interval (1, 2) thus resolving a conjecture of Jackson’s in the negat...

Ngày tải lên: 07/08/2014, 13:21

... journal of combinatorics 15 (2008), #R4 11 The Minor Crossing Number of Graphs with an Excluded Minor Drago Bokal Department of Combinatorics and Optimization University of Waterloo Waterloo, Canada dbokal@uwaterloo.ca Gaˇsper ... Pinontoan and R. Bruce Richter. Crossing numbers of sequences of graphs. II. Planar tiles. J. Graph Theory, 42(4):332–341, 2003. [33...

Ngày tải lên: 07/08/2014, 15:22

... combinatorics 14 (2007), #R 51 10 Table II. Bounds on K(r, s, s; 2) for r ≤ 16 and 9 ≤ s ≤ 16 . s = 9 s = 10 s = 11 s = 12 s = 13 s = 14 s = 15 s = 16 r = 1 9 10 11 12 13 14 15 16 r = 2 16 B 18 B 20B ... 71F 72F a85E a96 − 98E a103 − 11 3E 11 0 − 12 6G r = 13 60 − 65C 66 − 72C 73 − 81F 79 − 84C 85F a98E 10 5 − 11 3E a 117 − 12 8E r = 14 63 − 67C 70 − 76C 77...

Ngày tải lên: 07/08/2014, 15:22

... most graphs on n vertices contain substantially many copies of any fixed graph, but contain no complete bipartite subgraphs with both parts larger than C log n, for some C > 0, independent of n. Hence, ... graph of order 2; - K 2 (s, t) for the complete bipartite graph with parts of size s and t; - f| X for the restriction of a map f to a set X. Specific notation Suppos...

Ngày tải lên: 07/08/2014, 15:23

... 10 LA 0 1 2 X 1 0 X 3 2 3 1 0 3 2 0 1 LB 0 1 2 X 1 0 X 3 2 3 0 1 3 2 1 0 LC 0 1 2 X 1 2 X 3 2 3 0 1 3 0 1 2 LD 0 1 2 X 1 3 X 0 2 0 1 3 3 2 0 1 LE 0 1 2 X 1 3 X 2 2 0 1 3 3 2 0 1 LF 0 2 1 X 1 ... 3 2 3 0 1 3 1 2 0 LG 0 2 1 X 1 3 X 0 2 1 0 3 3 0 2 1 LH 0 2 1 X 1 3 X 0 2 0 3 1 3 1 0 2 LI 0 2 1 X 1 3 X 2 2 0 3 1 3 1 2 0 LJ...

Ngày tải lên: 07/08/2014, 15:23

... t  2 (m−2−ν)(n−n 0 −···−n 2 m−2 −1)+n 0 +···+n 2 m−2 −1 . Proof. The formulas follow from Corollary 3.2 and simple counting arguments. 4 B n -orbits in Tuples of Dihedral Groups The dihedral group D N of order 2N is given by the ... (2008), #R80 2 Hurwitz Equivalence in Tuples of Generalized Quaternion Groups and Dihedral Groups Xiang-dong Hou Department...

Ngày tải lên: 07/08/2014, 21:20

... 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

... families of pairs of graphs which share the same zeta function. 1. Introduction In 2009 , Cooper described an infinite family of non-isomorphic pairs of graphs which she conjectured had the same Ihara ... 2010 Mathematics Subject Classification: 05C38 Abstract In 2009, Cooper presented an infinite family of pairs of graphs which were con- jectured to have t...

Ngày tải lên: 08/08/2014, 12:22

... coverings of these gives infinitely many hypermaps of type (l, m, n) and genus g  3. In particular, taking m = 2, if we can construct infinitely many planar maps of a given type, each with at least ... and −1 + i, the vertex at 2 to 0 and 1 + i, and the vertex at 2i to 1 + i and −1 + i. We have then, a t this stage, three triangular faces and one face of vale...

Ngày tải lên: 08/08/2014, 12:23

... Table 4 Safety data of patients receiving aprotinin and tranexamic acid Aprotinin Tranexamic acid P Myocardial infarction (ICU) All patients N 8 6 0.78 Open-heart procedures 0 2 0.04 All patients ... erning t he treatment with and, if treated, how many Table 1 Baseline characteristics of the patients in the aprotinin and tranexamic acid groups Aprotinin Tra...

Ngày tải lên: 13/08/2014, 21:21