Báo cáo toán học: "Values of Domination Numbers of the Queen’s Graph" pdf

... denote the edge between the two vertices x and the electronic journal of combinatorics 15 (2008), #R49 1 Let n ≥ 2 and let E r and E b be as in the proof of lemma 1. Let S be the set of all n-ary ... and (ii) are, and so we make no further mention of it. 3 Proof of theorem 1 Let k ∈ N and let [3k − 4] k denote the collection of k-subsets of [3k − 4]. Let G be the c...

Ngày tải lên: 07/08/2014, 15:23

... measured. The percentage of reduction in the paw volume was calculated by subtracting the difference between the right and left hind paw volumes in the treated group from the difference in the control ... Anti-inflammatory activity The pharmacological evaluation of the tested compounds (2–4) was carried out as per the protocol specified. The anti-inflammatory acti...

Ngày tải lên: 20/06/2014, 20:20

... inserting just (1 + ε)n edges. 2 Main Results In the following we denote the edge set of G n,i by E i . The vertex set of the process is denoted by V . The set of open pairs in G n,i is called O i and ... edges. In addition to the number of open pairs, our proof only requires the number of partial vertices for all non-adjacent pairs {u, v}. We denote the set of par...

Ngày tải lên: 08/08/2014, 14:23

... for domination numbers of the queen’s graph, to appear in Discrete Math. [19] W. D. Weakley, A lower bound for domination numbers of the queen’s graph, submitted. the electronic journal of combinatorics ... squares of column −59 and row 59 of Q 119 are covered, so a copy of Q 118 is dominated. the electronic journal of combinatorics 8 (2001), #R29 16 Values...

Ngày tải lên: 07/08/2014, 06:22

... coverings of the integers given the m k ) and minimize the a’s and b’s con- structed by Knuth’s method. Thus the minimum values of a and b are determined for the pairs (p k ,m k ). 2 Proof of Regularity Before ... c 1 . Note that for the m k abovetobeabletocovertheintegersn≡c 1 (mod 64), then they divided by their greatest common divisor with 64 must cover all of the int...

Ngày tải lên: 07/08/2014, 06:20

... bijection between the set of compositions of n −2by{1, 2} and the set of compositions of n − 1 by odd numbers. The bijection works by prepending a 1 to a composition of the former type, and then performing ... pictures of weight k.Acard of weight k is a pair consisting of a picture of weight k and a k-element subset of N that we will call the label set of the...

Ngày tải lên: 07/08/2014, 06:20

... Furthermore, ∆(G  ) ≥ 3 as the link vertex in the copy of X has degree at least three. The components of G  [S  ], other than the P 2 -component consisting of the two degree-2 vertices in the ... cycle. The three types of units are shown in Figure 2. the electronic journal of combinatorics 14 (2007), #R65 8 the link vertex and a neighbor of the link vertex i...

Ngày tải lên: 07/08/2014, 15:23

... give the to t al w-weight of all o f the members of L(n), the left-hand side by Theorem 5.1. As for the right-hand side, observe that the k-th term of the sum gives the total weight of all of the ... undisturbed. Note that the ordering of B on the right has one more non-record low (the c) than the one of the left, whence the nrec values of the corr...

Ngày tải lên: 08/08/2014, 14:23

... 18 (2011), #P158 32 Proof of Theo rem 44. The proof is almost identical with the one of Theorem 43. We only need to modify the row µ = (1, 1) in the table (6.2). Instead of using E (1,1) ∈ D ′ (which contains ... construction of a basis for M d 1 ,d 2 . The Main Theorem follows immediately from Theorem 44 in §6.2 and Theorem 55 in §7. The construction of the basis for...

Ngày tải lên: 08/08/2014, 14:23

... delay, in the computation of the RE we are not conditioning on the fact of reaching the N-th node of the network, i.e., the last reachable node of the network. Therefore, also the packets which stop ... nodes, until (in the case of a successful forwarding) only one of them reaches 0, say the k-th BC. During a transmission of a node the other BCs freeze. Sho...

Ngày tải lên: 20/06/2014, 20:20