Topological Structure of Non-wandering Set of a Graph Map

Let G be a graph （i.e., a finite one-dimensional polyhedron） and f ： G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulation point of the set of non-wandering points of f with infinite orbit is a two-order accumulation point of the set of recurrent points of f; the derived set of an ω-limit set of f is equal to the derived set of an the set of recurrent points of f; and the two-order derived set of non-wandering set of f is equal to the two-order derived set of the set of recurrent points of f.     

Panconnectivity for interconnection networks with faulty elements

Let Go and G1 be two graphs with the same vertices. The new graph G（G0, G1; M） is a graph with the vertex set V（0o） ∪）V（G1） and the edge set E（Go） UE（G1） UM, where M is an arbitrary perfect matching between the vertices of Go and G1, i.e., a set of cross edges with one endvertex in Go and the other endvertex in G1. In this paper, we will show that if Go and G1 are f-fault q-panconnected, then for any f 〉 2, G（G0, G1; M） is （f ＋ 1）-fault （q ＋ 2）-panconnected.     

Vertex-distinguishing IE-total Colorings of Cycles and Wheels

Let G be a simple graph. An IE-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C（u） be the set of colors of vertex u and edges incident to u under f. For an IE-total coloring f of G using k colors, if C（u）=C（v） for any two different vertices u and v of V （G）, then f is called a k-vertex-distinguishing IE-total-coloring of G, or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χievt（G）, and is called the VDIET chromatic number of G. We get the VDIET chromatic numbers of cycles and wheels, and propose related conjectures in this paper.     

完全图的Cantesian积的L(2,1)-圆标定

For positive integers j and k with j ≥ k, an L（j, k）-labeling of a graph G is an assignment of nonnegative integers to V（G） such that the difference between labels of adjacent vertices is at least j, and the difference between labels of vertices that are distance two apart is at least k. The span of an L（j, k）-labeling of a graph G is the difference between the maximum and minimum integers it uses. The λj, k-number of G is the minimum span taken over all L（j, k）-labelings of G. An m-（j, k）-circular labeling of a graph G is a function f ： V（G） →{0, 1, 2,..., m - 1} such that ｜f（u） - f（v）｜m ≥ j if u and v are adjacent; and ｜f（u） - f（v）｜m 〉 k ifu and v are at distance two, where ｜x｜m = min{｜xl｜, m-｜x｜}. The minimum integer m such that there exists an m-（j, k）-circular labeling of G is called the σj,k-number of G and is denoted by σj,k（G）. This paper determines the σ2,1-number of the Cartesian product of any three complete graphs.     

Typical Frobenius coverings

A covering p from a Cayley graph Cay（G, X） onto another Cay（H, Y） is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p ： G →H is a group epimorphism. In this paper, we emphasize on the typical Frobenius coverings of Cay（H, Y）. We show that any typical Frobenius covering Cay（G, X） of Cay（H, Y） can be derived from an epimorphism /from G to H which is determined by an automorphism f of H. If Cay（G, X1） and Cay（G, X2） are two isomorphic typical Frobenius coverings under a graph isomorphism Ф, some properties satisfied by Фare given.     

The Asymptotic Average Shadowing Property and Its Applications

Let （X, d） be a bounded metric space and f ： X → X be a uniformly continuous surjection. For a given dynamical system （X, f） which may not be compact, we investigate the relation between the asymptotic average shadowing property（AASP）, transitivity and mixing. If f has the AASP, then the following statements hold： （1） f n is chain transitive for every positive integer n; （2） If X is compact and f is an expansive homeomorphism, then f is topologically weakly mixing; （3） If f is equicontinuous, then f is topologically weakly mixing; （4） If X is compact and f is equicontinuous, then f ×f is a minimal homeomorphism. We also show that the one-sided shift map has the AASP and the identity map 1 X does not have the AASP. Furthermore, as its applications, some examples are given.     

A Family of Non-quasiprimitive Graphs Constructed From PSU3（q） Where q Is Odd

Let Г be a simple connected graph and let G be a group of automorphisms of Г. Г is said to be （G, 2）-arc transitive if G is transitive on the 2-arcs of Г. It has been shown that there exists a family of non-quasiprimitive （PSU3（q）, 2）-arc transitive graphs where q = 2^3m with m an odd integer. In this paper we investigate the case where q is an odd prime power.     

The boundary behavior of domains with complete translating,minimal and CMC graphs in N~2×R

In this paper,we discuss graphs over a domain ??N~2 in the product manifold N~2×R.Here N~2is a complete Riemannian surface and?has piecewise smooth boundary.Letγ???be a smooth connected arc andΣbe a complete graph in N~2×R over?.We show that ifΣis a minimal or translating graph,thenγis a geodesic in N~2.Moreover ifΣis a CMC graph,thenγhas constant principal curvature in N~2.This explains the infinity value boundary condition upon domains having Jenkins-Serrin theorems on minimal and constant mean curvature(CMC)graphs in N~2×R.     

On （g, f）-Uniform Graphs

A graph G is called a (g, f)-uniform graph if for each edge of G, there is a (g, f)-factor containing it and another (g, f)-factor excluding it. In this paper a necessary and sufficient condition for a graph to be a (g, f)-uniform graph is given and some applications of this condition are discussed. In particular, some simple sufficient conditions for a graph to be an [a, b]-uniform graph are obtained for a≤b.     

联图C_mVG_n的邻点可区别Ｅ-全染色(英文)

Let G（V, E） be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G（abbreviated to k-AVDETC）, if for uv ∈ E（G）, we have f（u） ≠ f（v）, f（u） ≠ f（uv）, f（v） ≠ f（uv）, C（u） ≠C（v）, where C（u） = {f（u）}∪{f（uv）|uv ∈ E（G）}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_at （G）. In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.     

SATURATION THEOREMS FOR GENERALIZED BERNSTEIN POLYNOMIALS

In the present paper, we give the explicit formula of the principal part of ∑k=0^n（{k}q-[n]qx）^sxk ∏m=0^n-k-1（1-q^mx） with respect to [n]q for any integer s and q ∈ （0, 1]. And, using the expressions, we obtain saturation theorems for Bn （f , qn,x） approximating to f（x） ∈ C[O, 1], 0 〈 qn ≤ 1, qn → 1.     

Approximation of Generalized Bernstein Operators

This paper is devoted to study direct and converse approximation theorems of the generalized Bernstein operators Cn( f,sn,x) via so-called unified modulus ω2φλ( f,t), 0 ≤λ≤1. We obtain main results as follows ω2φλ( f,t) =O(tα)|Cn( f,sn,x)- f(x)| =O(n-12 δ1-λn(x))α,where δ2n(x) =max{φ2(x),1/n} and 0 α 2.     

Ricci Curvature of Certain Submanifolds in Kenmotsu Space Forms

In this paper, we obtain some sharp inequalities between the Ricci cur- vature and the squared mean curvature for bi-slant and semi-slant submanifolds in Kenmotsu space forms. Estimates of the scalar curvature and the k-Ricci curvature, in terms of the squared mean curvature, are also proved respectively.     

Some classes of Kenmotsu manifolds with respect to semi-symmetric metric connection

In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semi-symmetric and φ-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection.     

Sharp upper bounds for \lambda _1^{L_r } of immersed hypersurfaces and their stability in space forms

In this paper we derive new sharp upper bounds for the first positive eigenvalue λ1^Lr of the linearized operator of the higher order mean curvature of a closed hypersurface immersed into a Riemannian space form R^（n＋l）（c） （c 〉 0）. Our bounds are extrinsic in the sense that they are given in terms of the higher order mean curvatures. Under the assumption Hr＋2 〉 0, by establishing two valuable integral formulas, we obtain unified sharp upper bounds of λ1^Lr. We also give an estimation of the upper bounds of the first eigenvalue of a SchrSdinger-type operator, by which we prove those hypersurfaces with positive constant Hr＋l in any space forms are stable if and only if they are geodesic spheres, thus generalizing the previous result obtained only in the case c≤0.     

VANISHING THEOREMS FOR ACH KAHLER MANIFOLDS AND HARMONIC MAPS

We discuss a class of complete Kaihler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincare inequality case and establish a vanishing theorem provided that the weighted function p is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincare inequality.     

S~4到CP~n的常曲率弱Lagrangian极小浸入

研究球面S~4到CP~n的常曲率弱Lagrangian极小浸入■:S~4→CP~n.如果■的诱导度量ds~2具有常(截面)曲率c,则存在一个整数s≥1,使得c=4/[s(s+3)].浸入■被两个四元齐次多项式f_s和f_(s-1)唯一确定.当s=1,即c=1,或s=2,即c=2/5时,浸入■是绝对实的.     

Uniqueness of grim hyperplanes for mean curvature flows

In this paper we show that an immersed nontrivial translating soliton for a mean curvature flow in \(\mathbb {R}^{n+1}\)(\(n=2,3)\) is a grim hyperplane if and only if it is mean convex and has weighted total extrinsic curvature of at most quadratic growth. For an embedded translating soliton \(\varSigma \) with nonnegative scalar curvature, we prove that if the mean curvature of \(\varSigma \) does not change signs on each end, then \(\varSigma \) must have positive scalar curvature unless it is either a hyperplane or a grim hyperplane.     

A Bernstein theorem for complete spacelike constant mean curvature hypersurfaces in Minkowski space

We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski space into the hyperbolic space. As an application, we prove a Bernstein theorem which says that if the image of the Gauss map is bounded from one side, then the spacelike constant mean curvature hypersurface must be linear. This result extends the previous theorems obtained by B. Palmer [Pa] and Y.L. Xin [Xin1] where they assume that the image of the Gauss map is bounded. We also prove a Bernstein theorem for spacelike complete surfaces with parallel mean curvature vector in four-dimensional spaces. Received July 4, 1997 / Accepted October 9, 1997     

Integral curvature estimates for F-stable hypersurfaces

We consider immersed hypersurfaces in euclidean which are stable with respect to an elliptic parametric functional with integrand F = F(N) depending on normal directions only. We prove an integral curvature estimate provided that F is sufficiently close to the area integrand, extending the classical estimate of Schoen, Simon and Yau [19] for stable minimal hypersurfaces in , as well as the pointwise estimate of Simon [22] for F-minimizing hypersurfaces. As a crucial point of our analysis we derive a generalized Simons inequality for the laplacian of the length of a weighted second fundamental form with respect to an abstract metric associated with F. As an application, we obtain a new Bernstein result for complete F-stable hypersurfaces of dimension .Received: 14 July 2003, Accepted: 13 September 2004, Published online: 10 December 2004Mathematics Subject Classification: 53C42, 49Q10, 35J60