共查询到20条相似文献,搜索用时 31 毫秒
1.
Dan Archdeacon 《Journal of Graph Theory》1986,10(3):385-401
A graph G is a k-amalgamation of two graphs G1 and G2 if G = G1 ∪ G2 and G1 ∩ G2 is a set of k vertices. In this paper we construct 3-amalgamations Gn = Hn ∪ Hn such that γ(Gn) = 5n and γ(Hn) = 3n, where γ denotes the orientable genus of a graph. Thus γ(G1 ∪ G2) may differ from γ(G1) + γ(G2) by an arbitrarily large amount for amalgamations over 3 (or more) vertices. In contrast, an earlier paper shows that the nonorientable genus of a k-amalgamation differs from the sum of the nonorientable genera of its parts by at most a quadratic on k. 相似文献
2.
Dan Archdeacon 《Journal of Graph Theory》1986,10(3):363-383
A graph G is a k-amalgamation of two graphs G1 and G2 if G = G1 ∪ G2 and G1 ∩G2 is a set of k vertices. In this paper we show that γ(G) differs from γ(G1) + γ(G2) by at most a quadratic on k, where γ denotes the nonorientable genus of a graph. In the sequel to this paper we show that no such bound holds for the orientable genus of k-amalgamations. 相似文献
3.
In 1963, Vizing [Vichysl.Sistemy 9 (1963), 30–43] conjectured that γ(G × H) ≥ γ(G)γ(H), where G × H denotes the cartesian product of graphs, and γ(G) is the domination number. In this paper we define the extraction number x(G) and we prove that P2(G) ≤ x(G), and γ(G × H) ≥ x(G)γ(H), where P2(G) is the 2-packing number of G. Though the equality x(G) = γ(G) is proven to hold in several classes of graphs, we construct an infinite family of graphs which do not satisfy this condition. Also, we show the following lower bound: γ(G × H) ≥ γ(G)P2(H) + P2(G)(γ(H) − P2(H)). © 1996 John Wiley & Sons, Inc. 相似文献
4.
We present various new inequalities involving the logarithmic mean L(x,y)=(x-y)/(logx-logy) L(x,y)=(x-y)/(\log{x}-\log{y}) , the identric mean I(x,y)=(1/e)(xx/yy)1/(x-y) I(x,y)=(1/e)(x^x/y^y)^{1/(x-y)} , and the classical arithmetic and geometric means, A(x,y)=(x+y)/2 A(x,y)=(x+y)/2 and G(x,y)=?{xy} G(x,y)=\sqrt{xy} . In particular, we prove the following conjecture, which was published in 1986 in this journal. If Mr(x,y) = (xr/2+yr/2)1/r(r 1 0) M_r(x,y)= (x^r/2+y^r/2)^{1/r}(r\neq{0}) denotes the power mean of order r, then $ M_c(x,y)<\frac{1}{2}(L(x,y)+I(x,y)) {(x,y>0,\, x\neq{y})} $ M_c(x,y)<\frac{1}{2}(L(x,y)+I(x,y)) {(x,y>0,\, x\neq{y})} with the best possible parameter c=(log2)/(1+log2) c=(\log{2})/(1+\log{2}) . 相似文献
5.
For any positive integer s, an s-partition of a graph G = (V, E) is a partition of E into E1 ∪ E2 ∪…? ∪ Ek, where ∣Ei∣ = s for 1 ≤ i ≤ k ? 1 and 1 ≤ ∣Ek∣ ≤ s and each Ei induces a connected subgraph of G. We prove
- (i) If G is connected, then there exists a 2-partition, but not necessarily a 3-partition;
- (ii) If G is 2-edge connected, then there exists a 3-partition, but not necessarily a 4-partition;
- (iii) If G is 3-edge connected, then there exists a 4-partition;
- (iv) If G is 4-edge connected, then there exists an s-partition for all s.
6.
Choonkil BAAK 《数学学报(英文版)》2006,22(6):1789-1796
Let X, Y be vector spaces. It is shown that if a mapping f : X → Y satisfies f((x+y)/2+z)+f((x-y)/2+z=f(x)+2f(z),(0.1) f((x+y)/2+z)-f((x-y)/2+z)f(y),(0.2) or 2f((x+y)/2+x)=f(x)+f(y)+2f(z)(0.3)for all x, y, z ∈ X, then the mapping f : X →Y is Cauchy additive.
Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras. 相似文献
7.
S. Haruki 《Aequationes Mathematicae》2002,63(3):201-209
Summary. Let (G, +) and (H, +) be abelian groups such that the equation 2u = v 2u = v is solvable in both G and H. It is shown that if f1, f2, f3, f4, : G ×G ? H f_1, f_2, f_3, f_4, : G \times G \longrightarrow H satisfy the functional equation f1(x + t, y + s) + f2(x - t, y - s) = f3(x + s, y - t) + f4(x - s, y + t) for all x, y, s, t ? G x, y, s, t \in G , then f1, f2, f3, and f4 are given by f1 = w + h, f2 = w - h, f3 = w + k, f4 = w - k where w : G ×G ? H w : G \times G \longrightarrow H is an arbitrary solution of f (x + t, y + s) + f (x - t, y - s) = f (x + s, y - t) + f (x - s, y + t) for all x, y, s, t ? G x, y, s, t \in G , and h, k : G ×G ? H h, k : G \times G \longrightarrow H are arbitrary solutions of Dy,t3g(x,y) = 0 \Delta_{y,t}^{3}g(x,y) = 0 and Dx,t3g(x,y) = 0 \Delta_{x,t}^{3}g(x,y) = 0 for all x, y, s, t ? G x, y, s, t \in G . 相似文献
8.
Gwang Hui Kim 《数学学报(英文版)》2009,25(1):29-38
The aim of this paper is to study the stability problem of the generalized sine functional equations as follows:
g(x)f(y)=f(x+y/2)^2-f(x-y/2)^2 f(x)g(y)=f(x+y/2)^2-f(x-y/2)^2,g(x)g(y)=f(x+y/2)^-f(x-y/2)^2
Namely, we have generalized the Hyers Ulam stability of the (pexiderized) sine functional equation. 相似文献
g(x)f(y)=f(x+y/2)^2-f(x-y/2)^2 f(x)g(y)=f(x+y/2)^2-f(x-y/2)^2,g(x)g(y)=f(x+y/2)^-f(x-y/2)^2
Namely, we have generalized the Hyers Ulam stability of the (pexiderized) sine functional equation. 相似文献
9.
Suppose C
r
= (r
C
r
) ∪ (r
C
r
+ 1 − r) is a self-similar set with r ∈ (0, 1/2), and Aut(C
r
) is the set of all bi-Lipschitz automorphisms on C
r
. This paper proves that there exists f* ∈ Aut(C
r
) such that
where and blip(g) = max(lip(g), lip(g
−1)).
This work was supported by National Natural Science Foundation of China (Grant Nos. 10671180, 10571140, 10571063, 10631040,
11071164) and Morningside Center of Mathematics 相似文献
10.
In a bounded simple connected region G ? ?3 we consider the equation $$L\left[ u \right]: = k\left( z \right)\left( {u_{xx} + u_{yy} } \right) + u_{zz} + d\left( {x,y,z} \right)u = f\left( {x,y,z} \right)$$ where k(z)? 0 whenever z ? 0.G is surrounded forz≥0 by a smooth surface Γ0 with S:=Γ0 ? {(x,y,z)|=0} and forz<0 by the characteristic \(\Gamma _2 :---(x^2 + y^2 )^{{\textstyle{1 \over 2}}} + \int\limits_z^0 {(---k(t))^{{\textstyle{1 \over 2}}} dt = 0} \) and a smooth surface Γ1 which intersect the planez=0 inS and where the outer normal n=(nx, ny, nz) fulfills \(k(z)(n_x^2 + n_y^2 ) + n_z^2 |_{\Gamma _1 } > 0\) . Under conditions on Γ1 and the coefficientsk(z), d(x,y,z) we prove the existence of weak solutions for the boundary value problemL[u]=f inG with \(u|_{\Gamma _0 \cup \Gamma _1 } = 0\) . The uniqueness of the classical solution for this problem was proved in [1]. 相似文献
11.
Tom Sanders 《Geometric And Functional Analysis》2011,21(1):141-221
Suppose that G is a finite group and f is a complex-valued function on G. f induces a (left) convolution operator from L
2(G) to L
2(G) by g ? f *g{g \mapsto f \ast g} where
f *g(z) : = \mathbbExy=zf(x)g(y) for all z ? G.f \ast g(z) := \mathbb{E}_{xy=z}f(x)g(y)\,\, {\rm for\,\,all} \, z \in G. 相似文献
12.
G. Kutyniok 《Archiv der Mathematik》2002,78(2):135-144
Let
r\mathbbR \rho_{\mathbb{R}} be the classical Schrödinger representation of the Heisenberg group and let L \Lambda be a finite subset of
\mathbbR ×\mathbbR \mathbb{R} \times \mathbb{R} . The question of when the set of functions
{t ? e2 pi y t f(t + x) = (r\mathbbR(x, y, 1) f)(t) : (x, y) ? L} \{t \mapsto e^{2 \pi i y t} f(t + x) = (\rho_{\mathbb{R}}(x, y, 1) f)(t) : (x, y) \in \Lambda\} is linearly independent for all
f ? L2(\mathbbR), f 1 0 f \in L^2(\mathbb{R}), f \neq 0 , arises from Gabor analysis. We investigate an analogous problem for locally compact abelian groups G. For a finite subset L \Lambda of G ×[^(G)] G \times \widehat{G} and rG \rho_G the Schrödinger representation of the Heisenberg group associated with G, we give a necessary and in many situations also sufficient condition for the set {rG (x, w, 1)f : (x, w) ? L} \{\rho_G (x, w, 1)f : (x, w) \in \Lambda\} to be linearly independent for all f ? L2(G), f 1 0 f \in L^2(G), f \neq 0 . 相似文献
13.
Abbas Najati 《数学学报(英文版)》2009,25(9):1529-1542
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation
f(x+y/2+z)-g(x-y/2+z)=h(y). This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 (1978). 相似文献 14.
Let G be a simple graph with n vertices and m edges. Let λ1, λ2,…, λn, be the adjacency spectrum of G, and let μ1, μ2,…, μn be the Laplacian spectrum of G. The energy of G is E(G) = n∑i=1|λi|, while the Laplacian energy of G is defined as LE(G) = n∑i=1|μi-2m/n| Let γ1, γ2, ~ …, γn be the eigenvalues of Hermite matrix A. The energy of Hermite matrix as HE(A) = n∑i=1|γi-tr(A)/n| is defined and investigated in this paper. It is a natural generalization of E(G) and LE(G). Thus all properties about energy in unity can be handled by HE(A). 相似文献
15.
Given a simple plane graph G, an edge‐face k‐coloring of G is a function ? : E(G) ∪ F(G) → {1,…,k} such that, for any two adjacent or incident elements a, b ∈ E(G) ∪ F(G), ?(a) ≠ ?(b). Let χe(G), χef(G), and Δ(G) denote the edge chromatic number, the edge‐face chromatic number, and the maximum degree of G, respectively. In this paper, we prove that χef(G) = χe(G) = Δ(G) for any 2‐connected simple plane graph G with Δ (G) ≥ 24. © 2005 Wiley Periodicals, Inc. J Graph Theory 相似文献
16.
Let G = (V, E) be a connected graph. A set D ? V is a set-dominating set (sd-set) if for every set T ? V ? D, there exists a nonempty set S ? D such that the subgraph 〈S ∪ T〉 induced by S ∪ T is connected. The set-domination number γs(G) of G is the minimum cardinality of a sd-set. In this paper we develop properties of this new parameter and relate it to some other known domination parameters. 相似文献
17.
As shown in [1] the simple group 2 D2m + 1 (3)^2 D_{2^m + 1} (3) is recognizable by spectrum. The main result of this paper generalizes the above, stating that 2 D2m + 1 (3)^2 D_{2^m + 1} (3) is recognizable by prime graph. In other words, we show that if G is a finite group satisfying G(G) = G(2 D2m + 1 (3))\Gamma (G) = \Gamma (^2 D_{2^m + 1} (3)) then G @ 2 D2m + 1 (3)G \cong ^2 D_{2^m + 1} (3). 相似文献
18.
《Quaestiones Mathematicae》2013,36(8):1101-1115
AbstractAn Italian dominating function (IDF) on a graph G = (V, E) is a function f: V → {0, 1, 2} satisfying the condition that for every vertex v ∈ V (G) with f (v) = 0, either v is adjacent to a vertex assigned 2 under f, or v is adjacent to at least two vertices assigned 1. The weight of an IDF f is the value ∑v∈V(G) f (v). The Italian domination number of a graph G, denoted by γI (G), is the minimum weight of an IDF on G. An IDF f on G is called a global Italian dominating function (GIDF) on G if f is also an IDF on the complement ? of G. The global Italian domination number of G, denoted by γgI (G), is the minimum weight of a GIDF on G. In this paper, we initiate the study of the global Italian domination number and we present some strict bounds for the global Italian domination number. In particular, we prove that for any tree T of order n ≥ 4, γgI (T) ≤ γI (T) + 2 and we characterize all trees with γgI (T) = γI (T) + 2 and γgI (T) = γI (T) + 1. 相似文献
19.
Ladislav Stacho 《Journal of Graph Theory》2001,36(2):117-120
We show that for any graph G, the chromatic number χ(G) ≤ Δ2(G) + 1, where Δ2(G) is the largest degree that a vertex ν can have subject to the condition that ν is adjacent to a vertex whose degree is at least as big as its own. Moreover, we show that the upper bound is best possible in the the following sense: If Δ2(G) ≥ 3, then to determine whether χ(G) ≤ Δ2(G) is an NP‐complete problem. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 117–120, 2001 相似文献
20.
Jing YANG Shi Xin LUO Ke Qin FENG 《数学学报(英文版)》2006,22(3):833-844
Assume that m ≥ 2, p is a prime number, (m,p(p - 1)) = 1,-1 not belong to 〈p〉 belong to (Z/mZ)^* and [(Z/mZ)^*:〈p〉]=4.In this paper, we calculate the value of Gauss sum G(X)=∑x∈F^*x(x)ζp^T(x) over Fq,where q=p^f,f=φ(m)/4,x is a multiplicative character of Fq and T is the trace map from Fq to Fp.Under our assumptions,G(x) belongs to the decomposition field K of p in Q(ζm) and K is an imaginary quartic abelian unmber field.When the Galois group Gal(K/Q) is cyclic,we have studied this cyclic case in anotyer paper:"Gauss sums of index four:(1)cyclic case"(accepted by Acta Mathematica Sinica,2003).In this paper we deal with the non-cyclic case. 相似文献
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