Let G admit an H-edge covering and f : V èE ? {1,2,?,n+e}{f : V \cup E \to \{1,2,\ldots,n+e\}} be a bijective mapping for G then f is called H-edge magic total labeling of G if there is a positive integer constant m(f) such that each subgraph Hi, i = 1, . . . , r of G is isomorphic to H and f(Hi)=f(H)=Sv ? V(Hi)f(v)+Se ? E(Hi)f(e)=m(f){f(H_i)=f(H)=\Sigma_{v \in V(H_i)}f(v)+\Sigma_{e \in E(H_i)} f(e)=m(f)}. In this paper we define a subgraph-vertex magic cover of a graph and give some construction of some families of graphs that admit this property. We show the construction of some
Cn- vertex magic covered and clique magic covered graphs. 相似文献
Let D be a bounded convex domain and Holc(D,D) the set of holomorphic maps from D to Cn with image relatively compact in D. Consider Holc(D,D) as a open set in the complex Banach space H∞n(D) of bounded holomorphic maps from D to Cn. We show that the map τ: Holc(D,D) → D (called the Heins map for D equals to the unit disc of C) which associates to ? ∈ Holc(D,D) its unique fixed point τ? ∈ D is holomorphic and its differential is given by dτ?(v) = (Id-dfτ(?))?1v(τ(?)) for v ∈ H∞n(D). 相似文献
Let nq(k, d) denote the smallest value of n for which there exists an [n, k, d; q]-code. It is known (cf. (J. Combin. Inform. Syst. Sci.18, 1993, 161–191)) that (1) n3(6, 195) {294, 295}, n3(6, 194) {293, 294}, n3(6, 193) {292, 293}, n3(6, 192) {290, 291}, n3(6, 191) {289, 290}, n3(6, 165) {250, 251} and (2) there is a one-to-one correspondence between the set of all nonequivalent [294, 6, 195; 3]-codes meeting the Griesmer bound and the set of all {v2 + 2v3 + v4, v1 + 2v2 + v3; 5, 3}-minihypers, where vi = (3i − 1)/(3 − 1) for any integer i ≥ 0. The purpose of this paper is to show that (1) n3(6, 195) = 294, n3(6, 194) = 293, n3(6, 193) = 292, n3(6, 192) = 290, n3(6, 191) = 289, n3(6, 165) = 250 and (2) a [294, 6, 195; 3]-code is unique up to equivalence using a characterization of the corresponding {v2 + 2v3 + v4, v1 + 2v2 + v3; 5, 3}-minihypers. 相似文献
The bandwidth problem for a graph G is to label its n vertices vi with distinct integers f(vi) so that the quantity max{| f(vi) ? f(vi)| : (vi vj) ∈ E(G)} is minimized. The corresponding problem for a real symmetric matrix M is to find a symmetric permutation M' of M so that the quantity max{| i ? j| : m'ij ≠ 0} is minimized. This survey describes all the results known to the authors as of approximately August 1981. These results include the effect on bandwidth of local operations such as refinement and contraction of graphs, bounds on bandwidth in terms of other graph invariants, the bandwidth of special classes of graphs, and approximate bandwidth algorithms for graphs and matrices. The survey concludes with a brief discussion of some problems related to bandwidth. 相似文献
A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant λ such that the equality λd(vi) = Σ(vi,vj)∈E(G) d(vj) holds for all i = 1, 2,..., |V(G)|, where d(vi) denotes the degree of vertex vi. Let ni denote the number of vertices with degree i. This paper deals with the 3-Hgraphs and determines their degree series. Moreover, the 3-Hgraphs with bounded ni (1 ≤ i ≤ 7) are studied and some interesting results are obtained. 相似文献
A model for cleaning a graph with brushes was recently introduced. Let α = (v1, v2, . . . , vn) be a permutation of the vertices of G; for each vertex vi let ${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}}${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}} and N-(vi)={j: vjvi ? E and j < i}{N^-(v_i)=\{j: v_j v_i \in E {\rm and} j<\,i\}} ; finally let ba(G)=?i=1n max{|N+(vi)|-|N-(vi)|,0}{b_{\alpha}(G)=\sum_{i=1}^n {\rm max}\{|N^+(v_i)|-|N^-(v_i)|,0\}}. The Broom number is given by B(G) = maxαbα(G). We consider the Broom number of d-regular graphs, focusing on the asymptotic number for random d-regular graphs. Various lower and upper bounds are proposed. To get an asymptotically almost sure lower bound we use a degree-greedy
algorithm to clean a random d-regular graph on n vertices (with dn even) and analyze it using the differential equations method (for fixed d). We further show that for any d-regular graph on n vertices there is a cleaning sequence such at least n(d + 1)/4 brushes are needed to clean a graph using this sequence. For an asymptotically almost sure upper bound, the pairing
model is used to show that at most n(d+2?{d ln2})/4{n(d+2\sqrt{d \ln 2})/4} brushes can be used when a random d-regular graph is cleaned. This implies that for fixed large d, the Broom number of a random d-regular graph on n vertices is asymptotically almost surely
\fracn4(d+Q(?d)){\frac{n}{4}(d+\Theta(\sqrt{d}))}. 相似文献
A hypersurface x : M → Sn+1 without umbilic point is called a Möbius isoparametric hypersurface if its Möbius form Φ = ?ρ?2∑i(ei(H) + ∑j(hij?Hδij)ej(log ρ))θi vanishes and its Möbius shape operator $ {\Bbb {S}}A hypersurface x : M → Sn+1 without umbilic point is called a M?bius isoparametric hypersurface if its M?bius form Φ = −ρ−2∑i(ei(H) + ∑j(hij−Hδij)ej(log ρ))θi vanishes and its M?bius shape operator ? = ρ−1(S−Hid) has constant eigenvalues. Here {ei} is a local orthonormal basis for I = dx·dx with dual basis {θi}, II = ∑ijhijθi⊗θi is the second fundamental form, and S is the shape operator of x. It is clear that any conformal image of a (Euclidean) isoparametric hypersurface in Sn+1 is a M?bius isoparametric hypersurface, but the converse is not true. In this paper we classify all M?bius isoparametric
hypersurfaces in Sn+1 with two distinct principal curvatures up to M?bius transformations. By using a theorem of Thorbergsson [1] we also show
that the number of distinct principal curvatures of a compact M?bius isoparametric hypersurface embedded in Sn+1 can take only the values 2, 3, 4, 6.
Received September 7, 2001, Accepted January 30, 2002 相似文献
For a fixed multigraph H with vertices w1,…,wm, a graph G is H-linked if for every choice of vertices v1,…,vm in G, there exists a subdivision of H in G such that vi is the branch vertex representing wi (for all i). This generalizes the notions of k-linked, k-connected, and k-ordered graphs.Given a connected multigraph H with k edges and minimum degree at least two and n7.5k, we determine the least integer d such that every n-vertex simple graph with minimum degree at least d is H-linked. This value D(H,n) appears to equal the least integer d′ such that every n-vertex graph with minimum degree at least d′ is b(H)-connected, where b(H) is the maximum number of edges in a bipartite subgraph of H. 相似文献
Let Xi, i ≥ 1, be a sequence of φ-mixing random variables with values in a sample space (X, A). Let L(Xi) = P(i) for all i ≥ 1 and let
n, n ≥ 1, be classes of real-valued measurable functions on (X, A). Given any function g on (X, A), let Sn(g) = Σi = 1n {g(Xi) − Eg(Xi)}. Under weak metric entropy conditions on
n and under growth conditions on both the mixing coefficients and the maximal variance V V(n) maxi ≤ n supgn ∫ g2 dP(i), we show that there is a numerical constant U < ∞ such that
Full-size image
a.s.
*, where
i = 1xP(i) and HH(n) is the square root of the entropy of the class
n. Additionally, the rate of convergence H−1(n/V)1/2 cannot, in general, be improved upon. Applications of this result are considered. 相似文献