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31.
Yongzhu Chen 《Discrete Mathematics》2008,308(18):4276-4279
Let r, k be positive integers, s(<r), a nonnegative integer, and n=2r-s+k. The set of r-subsets of [n]={1,2,…,n} is denoted by [n]r. The generalized Kneser graph K(n,r,s) is the graph whose vertex-set is [n]r where two r-subsets A and B are joined by an edge if |A∩B|?s. This note determines the diameter of generalized Kneser graphs. More precisely, the diameter of K(n,r,s) is equal to , which generalizes a result of Valencia-Pabon and Vera [On the diameter of Kneser graphs, Discrete Math. 305 (2005) 383-385]. 相似文献
32.
Toru Kojima 《Discrete Mathematics》2008,308(7):1282-1295
The bandwidth B(G) of a graph G is the minimum of the quantity max{|f(x)-f(y)|:xy∈E(G)} taken over all proper numberings f of G. The strong product of two graphs G and H, written as G(SP)H, is the graph with vertex set V(G)×V(H) and with (u1,v1) adjacent to (u2,v2) if one of the following holds: (a) u1 and v1 are adjacent to u2 and v2 in G and H, respectively, (b) u1 is adjacent to u2 in G and v1=v2, or (c) u1=u2 and v1 is adjacent to v2 in H. In this paper, we investigate the bandwidth of the strong product of two connected graphs. Let G be a connected graph. We denote the diameter of G by D(G). Let d be a positive integer and let x,y be two vertices of G. Let denote the set of vertices v so that the distance between x and v in G is at most d. We define δd(G) as the minimum value of over all vertices x of G. Let denote the set of vertices z such that the distance between x and z in G is at most d-1 and z is adjacent to y. We denote the larger of and by . We define η(G)=1 if G is complete and η(G) as the minimum of over all pair of vertices x,y of G otherwise. Let G and H be two connected graphs. Among other results, we prove that if δD(H)(G)?B(G)D(H)+1 and B(H)=⌈(|V(H)|+η(H)-2)/D(H)⌉, then B(G(SP)H)=B(G)|V(H)|+B(H). Moreover, we show that this result determines the bandwidth of the strong product of some classes of graphs. Furthermore, we study the bandwidth of the strong product of power of paths with complete bipartite graphs. 相似文献
33.
Average Width and Optimal Recovery of Some Anisotropic Classes of Smooth Functions Defined on the Euclidean Space R~d 总被引:1,自引:0,他引:1
§ 1.Introduction and Main Results In[1 ] ,[2 ] ,the authors studied some problems of optimal recovery of functions de-fined on a cube,for a class of functions with partial derivatives of a fixed order havingmoduli of continuity not exceeding a given modules of continuity,and for the unit ballsSHαp in the spaces Hαp satisfying the mixed Holder conditionα,respectively.They ob-tained some weak asymptotic results. In[3 ] ,[4 ] and[5] ,Magarill-Il' yaev,Liu and Sun studied some proble… 相似文献
34.
He-Xi Ye 《Discrete Mathematics》2009,309(4):1001-3257
Let f(t,k) be the maximum diameter of graphs obtained by deleting t edges from a (t+1)-edge-connected graph with diameter k. This paper shows for t≥4, which corrects an improper result in [C. Peyrat, Diameter vulnerability of graphs, Discrete Appl. Math. 9 (3) (1984) 245-250] and also determines f(2,k)=3k−1 and f(3,k)=4k−2 for k≥3. 相似文献
35.
Li-Ping Huang 《Geometriae Dedicata》2009,138(1):1-12
Let R, S be Bezout domains. Assume that n is an integer ≥ 3, 1 ≤ k ≤ n − 2. Denoted by the k-dimensional Grassmann space on . Let be a map. This paper proves the following are equivalent: (i) is an adjacency preserving bijection in both directions. (ii) is a diameter preserving bijection in both directions. Moreover, Chow’s theorem on Grassmann spaces over division rings is
extended to the case of Bezout domains: If is an adjacency preserving bijection in both directions, then is induced by either a collineation or the duality of a collineation.
Project 10671026 supported by National Natural Science Foundation of China. 相似文献
36.
The bounded edge-connectivity λk(G) of a connected graph G with respect to is the minimum number of edges in G whose deletion from G results in a subgraph with diameter larger than k and the edge-persistence D+(G) is defined as λd(G)(G), where d(G) is the diameter of G. This paper considers the Cartesian product G1×G2, shows λk1+k2(G1×G2)≥λk1(G1)+λk2(G2) for k1≥2 and k2≥2, and determines the exact values of D+(G) for G=Cn×Pm, Cn×Cm, Qn×Pm and Qn×Cm. 相似文献
37.
Ioan Tomescu 《Discrete Mathematics》2009,309(9):2745-788
The degree distance of a connected graph, introduced by Dobrynin, Kochetova and Gutman, has been studied in mathematical chemistry. In this paper some properties of graphs having minimum degree distance in the class of connected graphs of order n and size m≥n−1 are deduced. It is shown that any such graph G has no induced subgraph isomorphic to P4, contains a vertex z of degree n−1 such that G−z has at most one connected component C such that |C|≥2 and C has properties similar to those of G.For any fixed k such that k=0,1 or k≥3, if m=n+k and n≥k+3 then the extremal graph is unique and it is isomorphic to K1+(K1,k+1∪(n−k−3)K1). 相似文献
38.
在研究EAP协议与Diameter协议的基础上,为解决分布式认证系统节点间会话一致性的问题,以及尽可能减少服务节点数量改变时产生的会话迁移数量,提出了一种基于消息的加权负载均衡算法(MOLB)。该算法使用散列法、虚拟节点和红黑树相结合的技术,实现了客户端请求在服务节点间的合理分布。Diameter网络环境中的实验结果表明:与其他常用的负载均衡算法相比,本文算法具有较小的负载均衡度和会话破坏度以及较低的会话破坏分布度。 相似文献
39.
40.
Rare earth composite cobalt ferrite ionic magnetic fluids were prepared by precipitation in the presence of Tri-sodium citrate. The sample phase, structure and particle sizes were determined by X-ray diffraction transmission and electron microscopy. It is clear that the particles appear as variously sized balls, Cobalt ferrite with sizes of 12-15 nm, Dysprosium cobalt ferrite and Yttrium cobalt ferrite with sizes of 6-8 nm. By adding rare earth ions, the average diameter of the magnetic nanoparticles was decreased. The decrease in diameter was explained using a micro-model of rare earth modification. The effect of rare earth ion modification on the saturation magnetization and magnetic induction of magnetic fluids was carried out using a Gouy magnetic balance and a spectrophotometer. The result shows that saturation magnetization and magnetic induction can be improved by adding Dy3+. By adding Y3+, magnetic induction was increased. However, the saturation magnetization then decreased. A theory of the mechanism of rare earth ion modification is discussed in detail. 相似文献