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1.
图的整数值控制函数 总被引：1，自引：0，他引：1
For an arbitrary subset P of the reals,a function f:V→P is defined to be a P-dominating function of a graph G=(V,E) if the sum of its function values over any closed neighbourhood is at least 1.That is,for every v∈V, f(N[v])≥1.The definition of total P-dominating function is obtained by simply changing‘closed’neighborhood N[v]in the definition of P-dominating function to‘open’neighborhood N(v).The (total) P-domination number of a graph G is defined to be the infimum of weight w(f) =∑_(v∈V)f(v) taken over all (total) P-dominating function f.Similarly,the P-edge and P-star dominating functions can be defined.In this paper we survey some recent progress oil the topic of dominating functions in graph theory.Especially,we are interested in P-,P-edge and P-star dominating functions of graphs with integer values. 相似文献
2.
For an arbitrary subset P of the reals, a function f ： V →P is defined to be a P-dominating function of a graph G = （V, E） if the sum of its function values over any closed neighbourhood is at least 1. That is, for every v ∈ V, f（N[v]） ≥ 1. The definition of total P-dominating function is obtained by simply changing ‘closed＇ neighborhood N[v] in the definition of P-dominating function to ‘open＇ neighborhood N（v）. The （total） P-domination number of a graph G is defined to be the infimum of weight w（f） = ∑v ∈ V f（v） taken over all （total） P-dominating function f. Similarly, the P-edge and P-star dominating functions can be defined. In this paper we survey some recent progress on the topic of dominating functions in graph theory. Especially, we are interested in P-, P-edge and P-star dominating functions of graphs with integer values. 相似文献
3.
图的符号全划分数 总被引：1，自引：0，他引：1
Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi（x） ≤ 1 for each x ∈ V, is called a signed total dominating family （of functions） on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s（G）. The properties of the signed total domatic number dt^s（G） are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs. 相似文献
4.
Let G=(V, E)be a simple graph without isolated vertices. For positive integer κ, a 3-valued function f:V → {-1, 0, 1} is said to be a minus total k-subdominating function(MTκSF)if ∑u∈N(u)f(u)≥ 1 for at least κ vertices v in G, where N(v)is the open neighborhood of v. The minus total κ-subdomination number γ-κt(G)equals the minimum weight of an MTkSF on G. In this paper, the values on the minus total κ-subdomination number of some special graphs are investigated. Several lower bounds on γ-κt of general graphs and trees are obtained. 相似文献
5.
《高等教育与学术研究》2007,(3)
A Romam dominating function on a graph G = (V , E) is a function f : V → {0,1,2} satisfying the condition that every vertex v for which f(v)=0 is adjacent to at least one vertex x for which f(x)=2, denoted by f = (V0 , V1 , V2). The weight of a Roman dominating function is the value f(V)=∑v∈V=2n2 n1, where |Vi|= ni (i=0,1,2), the minimum weight of a Ronam dominating function denoted by γ R (G ). In this paper, we give an upper bound of γ R (G ), and at the same time, we answer an open problem posed in [1]. 相似文献
6.
许承德 《上海大学学报(英文版)》2005,(4)
1IntroductionIn general,we followthe notation and terminologyin Refs.[1-5,7].In this paper all graphs are si mple.LetGbe a graph,V(G)the vertex set ofG,andE(G)the edge set ofG.The distance between twoverticesx,y∈V(G)is denoted bydG(x,y).Thediameter ofGis denoted byd(G).A short(x,y)-pathis an(x,y)-path with length≤d(G).An edgee∈E(G)is called cyclic if there exists a cycle inGcontaininge.To each cyclic edgee,letg(e)be thelength of the shortest cycle containinge.Ifeis abridge theng(e)… 相似文献
7.
A graph is called claw-free if it does not contain a claw as its induced subgraph. In this paper, we prove the following results : 1 ) If G is a 2-connected claw-free graph on n vertices, then for any vertex υ and any two distinct vertices x and y in V(G) - |υ| , G has a path containing v and all neighbors of v and connecting x and y;2) Let C be the longest cycle in a 3-connected claw-free graph G and H a component of G - C,and if H is connected but not 2-connected, then there exist nonadjacent vertices u and v in H such that |V(C)| ≥3(d(u) d(u)) -2. 相似文献
8.
Let G = （V,A） be a digraph.A set T of vertices of G is a twin dominating set of G if for every vertex v ∈ V ／ T.There exist u,w ∈ T （possibly u = w） such that （u,v）,（v,w） ∈ A.The twin domination number γ＊（G） of G is the cardinality of a minimum twin dominating set of G.In this paper we consider the twin domination number in generalized Kautz digraphs GK（n,d）.In these digraphs,we establish bounds on the twin domination number and give a sufficient condition for the twin domination number attaining the lower bound.We give the exact values of the twin domination numbers by constructing minimum twin dominating sets for some special generalized Kautz digraphs. 相似文献
9.
设图G=G(V,E),令函数f:V→{-1,1},f的权w(f)=∑v∈Vf[v],对v∈V,定义f[v]=∑u∈N[v]f(u),这里N[v]表示V中顶点v及其邻点的集合。图G的符号控制函数为f:V→{-1,1}满足对所有的v∈V有f[v]≥1,图G的符号控制数γs(G)就是图G上符号控制数的最小权,称其f为图G的γs-函数。研究了C2n图,通过给出它的一个γs-函数得到了其符号控制数。 相似文献
10.
Given a graph G,a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and |C|≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted as TC (G), is the minimum cardinality of a clique-transversal set in G. The clique-graph of G, denoted as K (G), is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques in G have nonempty intersection. Let F be a class of graphs G such that F={G|K(G) is a tree}. In this paper the graphs in F having independent clique-transversal sets are shown and thus TC (G)/|G|≤1/2 for all G ∈ F. 相似文献
11.
Ｉｎ 1935 ,Ｐ .Ｅｒｄ¨ｏｓａｎｄＧＳｚｅｋｅｒｅｓｏｂｔａｉｎｅｄｔｈｅｃｌａｓｓｉｃａｌｉｎｅｑｕａｌｉｔｙＲ (ｍ ,ｎ)≤Ｒ (ｍ - 1,ｎ) Ｒ(ｍ ,ｎ - 1) . Ｉｎ 196 8,Ｋ .ＷａｌｋｅｒｐｒｏｖｅｄｔｈａｔＲ(ｎ ,ｎ)≤ 4Ｒ(ｎ- 2 ,ｎ) 2 . Ｉｎ 1998,ＨｕａｎｇＹ .Ｒ .ａｎｄＺｈａｎｇＫ .Ｍ .[1,2 ] ｐｒｏｖｅｄｔｈａｔＲ(ｍ ,ｎ)≤ 12 (β 3γ 5 ) 12 γ(4α 2 β - 3γ 6 ) (β 1) 2 Ｉｎｔｈｉｓｐａｐｅｒ ,ｗｅｏｂｔａｉｎｓｏｍｅｎｅｗｕｐｐｅｒｂｏｕｎｄｓｆｏｒＲ(ｍ ,ｎ ,ｌ)ａｎｄＲ(ｍ … 相似文献
12.
In an effort to find the effect of mass transfer ,surface tesion and drag forces on the velocity distribution,the mathematical model of the velocity profile of a nascent hollow fiber during membrane formation in the air gap region was numerically simulated by using the Runge-Kutta method (fourth-order method).The effect of mass transfer on velocity distribution based on the complicated function(G(Ch^s))was presented and the dffects of a complicated function were studied in two cases:in the first case,G(Ch^s) was constant;in the second,G(Ch^s) was variable.The latter was done by varying with the concentration of solvent in a nascent hollow fiber through the air-gap region.One empirical equation was used to describe this change and the predected values had a better agreement with the experimental values.To verify the moedl hypotheses,hollow fiber membranes were spun from 20:80 polybenzimidazole/polyetherimide dopes with 25.6 wt％ solid in N,N-dimethylacetamide (DMAc) using water as the external and internal coagulants.Based on the experimental results of dry-jet wet-spinning process for the fabrication of hollow fiber membranes,it is found that the model calculated values were in a good agreement with the experimental values. 相似文献
13.
HAN Jing-wei YU Yao-yong 《浙江大学学报(A卷英文版)》2007,8(6):963-968
In this work, we study the Asanov Finsler metric F=α(β2/α2 gβ/α 1)1/2exp{(G/2)arctan[β/(hα) G/2]}, where α=(αijyiyj)1/2 is a Riemannian metric and β=biyj is a 1-form, g∈(-2,2), h=(1-g2/4)1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α. 相似文献
14.
Let R be a ring, a ,b ∈ R, ( D , α ) and (G , β ) be two generalized derivations of R . It is proved that if aD ( x ) = G ( x )b for all x ∈ R, then one of the following possibilities holds: (i) If either a or b is contained in C , then α = β= 0 and there exist p , q ∈ Qr ( RC) such that D ( x )= px and G ( x )= qx for all x ∈ R;(ii) If both a and b are contained in C , then either a = b= 0 or D and G are C-linearly dependent;(iii) If neither a nor b is contained in C , then there exist p , q ∈ Qr ( RC) and w ∈ Qr ( R) such that α ( x ) = [ q ,x] and β ( x ) = [ x ,p] for all x ∈ R, whence D ( x )= wx-xq and G ( x )= xp + avx with v ∈ C and aw-pb= 0. 相似文献
15.
ZAKHARENKO A.A. 《浙江大学学报(A卷英文版)》2007,8(4):669-674
Acoustic wave propagation in piezoelectric crystals of classes?43m and 23 is studied. The crystals Tl3VS4 and Tl3TaSe4 (43m) of the Chalcogenide family and the crystal Bi12TiO20 (23) possess strong piezoelectric effect. Because the surface Bleustein-Gulyaev waves cannot exist in piezoelectric cubic crystals, it was concluded that new solutions for shear-horizontal surface acoustic waves (SH-SAWs) are found in the monocrystals using different electrical boundary conditions such as electri- cally “short” and “open” free-surfaces for the unique [101] direction of wave propagation. For the crystal Tl3TaSe4 with coefficient of electromechanical coupling (CEMC) Ke2=e2/(C×g)～1/3, the phase velocity Vph for the new SH-SAWs can be calculated with the following formula: Vph=(Va Vt)/2, where Vt is the speed of bulk SH-wave, Vt=Vt4(1 Ke2)1/2, Va=aKVt4, aK=2[Ke(1 Ke2)1/2-Ke2]1/2, and Vt4=(C44/ρ)1/2. It was found that the CEMC K2 evaluation for Tl3TaSe4 gave the value of K2=2(Vf–Vm)/Vf～0.047 (～4.7%), where Vf～848 m/s and Vm~828 m/s are the new-SAW velocities for the free and metallized surfaces, respectively. This high value of K2(Tl3TaSe4) is significantly greater than K2(Tl3VS4)～3% and about five times that of K2(Bi12TiO20). 相似文献
16.
The big upper bound of typical van der Waerden number was investigated through calculating the van der Waerden number on a circle. And the van der Waerden number Wh (3,3) = 9, Wh (3,3,3)≥25 on a circle was calculated by computer. 相似文献
17.
The seed method is used for solving multiple linear systems A^(i) x^(i) = b^(i) for l≤ i≤ s , where the coefficient matrix A^(i) and the right-hand side b^(i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A^(i) . In this paper, the FOM method is employed to solve multiple linear systems when coefficient matrices are non-symmetric matrices. One of the systems is selected as the seed system which generates a Krylov subspace, then the residuals of other systems are projected onto the generated Krylov subspace to get the approximate solutions for the unsolved ones. The whole process is repeated until all the systems are solved. 相似文献
18.
This paper considers the synchronization of solutions for lattices of the coupled non-autonomous Chen system. By using the
Lyapunov function, we show that when the second coupled operator is negative definite self-adjoint and its coefficient is
suitable large, the Chen coupled lattice system is bounded dissipative (In particular, the solutions for lattices of the coupled
autonomous Chen system converge to zero as t → ∞). The synchronization between any two solutions of the coupled Chen system can be slaved only by coefficients in the
x- or y-component for the suitably large second coupled coefficient. Finally, some numerical simulations are given.
Project supported by the National Natural Science Foundation of China (Grant No.10771139) 相似文献
19.
Let Bnp={x ∈ Rn‖|x ‖p≤l} be the unit ball ofp norm in the n-dimensional normed space p. The formula for the volume of Bnp was obtained and its asymptotic properties were found out as n→∞and p→∞. 相似文献