共查询到20条相似文献,搜索用时 125 毫秒
1.
Let ind(G) be the number of independent sets in a graph G. We show that if G has maximum degree at most 5 then
ind(G) £ 2iso(G) ?uv ? E(G) ind(Kd(u),d(v))\frac1d(u)d(v){\rm ind}(G) \leq 2^{{\rm iso}(G)} \prod_{uv \in E(G)} {\rm ind}(K_{d(u),d(v)})^{\frac{1}{d(u)d(v)}} 相似文献
2.
Let 𝒲 be the Virasoro-like algebra, and d 1, d 2 be the degree derivations of 𝒲. Set ? = W⊕C d 1⊕C d 2. Let F α(V) be the ?-module defined by Larsson's functor applied to a finite dimensional sl 2-module V. In this article, the derivations from ? to ?-modules F α(V) and the first cohomology group H 1(?, F α(V)) are given. 相似文献
3.
Michael Klemm 《Journal of Combinatorial Theory, Series A》1984,36(3):364-372
Let d be the minimum distance of an (n, k) code , invariant under an abelian group acting transitively on the basis of the ambient space over a field F with char F × n. Assume that contains the repetition code, that dim( ∏ ⊥) = k ? 1 and that the supports of the minimal weight vectors of form a 2-design. Then d2 ? d + 1 ? n with equality if and only if the design is a projective plane of order d ? 1. The case d2 ? d + 1 = n can often be excluded with Hall's multiplier theorem on projective planes, a theorem which follows easily from the tools developed in this paper Moreover, if d2 ? d + 1 > n and F = GF(2) then (d ? 1)2 ? n. Examples are the generalized quadratic residue codes. 相似文献
4.
Gary Chartrand Garry L. Johns Songlin Tian Steven J. Winters 《Journal of Graph Theory》1993,17(4):509-521
The directed distance dD(u, v) from a vertex u to a vertex v in a strong digraph D is the length of a shortest (directed) u - v path in D. The eccentricity of a vertex v in D is the directed distance from v to a vertex furthest from v. The distance of a vertex v in D is the sum of the directed distances from v to the vertices of D. The center C(D) of D is the subdigraph induced by those vertices of minimum eccentricity, while the median M(D) of D is the subdigraph induced by those vertices of minimum distance. It is shown that for every two asymmetric digraphs D1 and D2, there exists a strong asymmetric digraph H such that C(H) ? D1 and M(H) ? D2, and where the directed distance from C(H) to M(H) and from M(H) to C(H) can be arbitrarily prescribed. Furthermore, if K is a nonempty asymmetric digraph isomorphic to an induced subdigraph of both D1 and D2, then there exists a strong asymmetric digraph F such that C(F) ? D1, M(F) ? D2 and C(F) ∩ M(F) ? K. © 1993 John Wiley & Sons, Inc. 相似文献
5.
Rubén A. Hidalgo 《Journal of Difference Equations and Applications》2013,19(9):953-969
Let Q be a m × m real matrix and f j : ? → ?, j = 1, …, m, be some given functions. If x and f(x) are column vectors whose j-coordinates are x j and f j (x j ), respectively, then we apply the finite dimensional version of the mountain pass theorem to provide conditions for the existence of solutions of the semilinear system Qx = f(x) for Q symmetric and positive semi-definite. The arguments we use are a simple adaptation of the ones used by Neuberger. An application of the above concerns partial difference equations on a finite, connected simple graph. A derivation of a graph 𝒢 is just any linear operator D:C 0(𝒢) → C 0(𝒢), where C 0(𝒢) is the real vector space of real maps defined on the vertex set V of the graph. Given a derivation D and a function F:V × ? → ?, one has associated a partial difference equation Dμ = F(v,μ), and one searches for solutions μ ∈ C 0(𝒢). Sufficient conditions in order to have non-trivial solutions of partial difference equations on any finite, connected simple graph for D symmetric and positive semi-definite derivation are provided. A metric (or weighted) graph is a pair (𝒢, d), where 𝒢 is a connected finite degree simple graph and d is a positive function on the set of edges of the graph. The metric d permits to consider some classical derivations, such as the Laplacian operator ?2. In (Neuberger, Elliptic partial difference equations on graphs, Experiment. Math. 15 (2006), pp. 91–107) was considered the nonlinear elliptic partial difference equations ?2 u = F(u), for the metric d = 1. 相似文献
6.
In this article we give the definition of the class ??1 and prove: (1) ??1(v) ≠ ? for v ∈ ?? = ??1 ∪ ??2 ∪ ??3 where (2) there exists 2 ? {2q2; q2 ± q, q2;q2 ± q} supplementary difference sets for q2 ∈ ??; (3) there exists an Hadamard matrix of order 4v for v ∈ ??; (4) if t is an order of T-matrices, there exists an Hadamard matrix of order 4tv for v ∈ ??. © 1994 John Wiley & Sons, Inc. 相似文献
7.
R. Peretz 《Journal of Mathematical Sciences》2010,168(3):428-436
Let
F ? \mathbbC[ X, Y ]2 F \in \mathbb{C}{\left[ {X,\,Y} \right]^2} be an étale map of degree deg F = d. An étale map
G ? \mathbbC[ X,Y ]2 G \in \mathbb{C}{\left[ {X,Y} \right]^2} is called a d-inverse approximation of F if deg G ≤ d and F ◦ G =(X + A(X, Y), Y + B(X, Y)) and G ◦ F =(X + C(X, Y), Y + D(X, Y)), where the orders of the four polynomials A, B, C, and D are greater than d. It is a well-known result that every
\mathbbC2 {\mathbb{C}^2} -automorphism F of degree d has a d-inverse approximation, namely, F
−1. In this paper, we prove that if F is a counterexample of degree d to the two-dimensional Jacobian conjecture, then F has no d-inverse approximation. We also give few consequences of this result. Bibliography: 18 titles. 相似文献
8.
It has been shown by Bogdanova and Boukliev [1] that there exist a ternary [38,5,24] code and a ternary [37,5,23] code. But it is unknown whether or not there exist a ternary [39,6,24] code and a ternary [38,6,23] code. The purpose of this paper is to prove that (1) there is no ternary [39,6,24] code and (2) there is no ternary [38,6,23] code using the nonexistence of ternary [39,6,24] codes. Since it is known (cf. Brouwer and Sloane [2] and Hamada and Watamori [14]) that (i) n3(6,23) = 38> or 39 and d3(38,6) = 22 or 23 and (ii) n3(6,24) = 39 or 40 and d3(39,6) = 23 or 24, this implies that n3(6,23) = 39, d3(38,6) = 22, n3(6,24) = 40 and d3(39,6) = 23, where n3<>(k,d) and d<>3(n,k) denote the smallest value of n and the largest value of d, respectively, for which there exists an [n,k,d] code over the Galois field GF(3). 相似文献
9.
10.
A word of length k over an alphabet Q of size v is a vector of length k with coordinates taken from Q. Let Q*4 be the set of all words of length 4 over Q. A T*(3, 4, v)‐code over Q is a subset C*? Q*4 such that every word of length 3 over Q occurs as a subword in exactly one word of C*. Levenshtein has proved that a T*(3, 4, vv)‐code exists for all even v. In this paper, the notion of a generalized candelabra t‐system is introduced and used to show that a T*(3, 4, v)‐code exists for all odd v. Combining this with Levenshtein's result, the existence problem for a T*(3,4, v)‐code is solved completely. © 2004 Wiley Periodicals, Inc. J Combin Designs 13: 42–53, 2005. 相似文献
11.
Given n vectors {i} ∈ [0, 1)d, consider a random walk on the d‐dimensional torus ??d = ?d/?d generated by these vectors by successive addition and subtraction. For certain sets of vectors, this walk converges to Haar (uniform) measure on the torus. We show that the discrepancy distance D(Q*k) between the kth step distribution of the walk and Haar measure is bounded below by D(Q*k) ≥ C1k?n/2, where C1 = C(n, d) is a constant. If the vectors are badly approximated by rationals (in a sense we will define), then D(Q*k) ≤ C2k?n/2d for C2 = C(n, d, j) a constant. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献
12.
A subset C of vertices in an undirected graph G = (V, E) is called a 1-identifying code if the sets I(v)={u C: d(u,v) 1 }, v V, are non-empty and no two of them are the same set. A 1-identifying code C is called 1-edge-robust 1-identifying if it is 1-identifying in every graph G1 obtained from G by deleting or adding one edge. It is shown that the optimal density of a 1-edge-robust 1-identifying code in the infinite triangular lattice is 3/7. 相似文献
13.
Satoru Fukasawa 《Geometriae Dedicata》2010,146(1):9-20
We consider the following problem: For a smooth plane curve C of degree d ≥ 4 in characteristic p > 0, determine the number δ(C) of inner Galois points with respect to C. This problem seems to be open in the case where d ≡ 1 mod p and C is not a Fermat curve F(p
e
+ 1) of degree p
e
+ 1. When p ≠ 2, we completely determine δ(C). If p = 2 (and C is in the open case), then we prove that δ(C) = 0, 1 or d and δ(C) = d only if d−1 is a power of 2, and give an example with δ(C) = d when d = 5. As an application, we characterize a smooth plane curve having both inner and outer Galois points. On the other hand,
for Klein quartic curve with suitable coordinates in characteristic two, we prove that the set of outer Galois points coincides
with the one of
\mathbbF2{\mathbb{F}_{2}} -rational points in
\mathbbP2{\mathbb{P}^{2}}. 相似文献
14.
Asaf Nachmias 《Geometric And Functional Analysis》2009,19(4):1171-1194
Let {G n } be a sequence of finite transitive graphs with vertex degree d = d(n) and |G n | = n. Denote by p t (v, v) the return probability after t steps of the non-backtracking random walk on G n . We show that if p t (v, v) has quasi-random properties, then critical bond-percolation on G n behaves as it would on a random graph. More precisely, if $\mathop {\rm {lim\, sup\,}} \limits_{n} n^{1/3} \sum\limits_{t = 1}^{n^{1/3}} {t{\bf p}^t(v,v) < \infty ,}$ then the size of the largest component in p-bond-percolation with ${p =\frac{1+O(n^{-1/3})}{d-1}}
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