共查询到20条相似文献,搜索用时 467 毫秒
1.
Inverse degree and edge-connectivity 总被引:2,自引:0,他引:2
Let G be a connected graph with vertex set V(G), order n=|V(G)|, minimum degree δ and edge-connectivity λ. Define the inverse degree of G as , where d(v) denotes the degree of the vertex v. We show that if
2.
Let H be a torsion-free strongly polycyclic (torsion-free virtually polycyclic, resp.) group. Let G be any group with maximal condition. We show that there exists a torsion-free strongly polycyclic (torsion-free virtually polycyclic, resp.) group and an epimorphism such that for any homomorphism ?:G→H, it factors through , i.e., there exists a homomorphism such that . We show that this factorization property cannot be extended to any finitely generated group G. As an application of factorization, we give necessary and sufficient conditions for N(f,g)=R(f,g) to hold for maps f,g:X→Y between closed orientable n-manifolds where π1(X) has the maximal condition, Y is an infra-solvmanifold, N(f,g) and R(f,g) denote the Nielsen and Reidemeister coincidence numbers, respectively. 相似文献
3.
Let ?n∈C∞(Rd?{0}) be a non-radial homogeneous distance function of degree n∈N satisfying ?n(tξ)=tn?n(ξ). For f∈S(Rd+1) and δ>0, we consider convolution operator associated with the smooth cone type multipliers defined by
4.
The pebbling number of a graph G, f(G), is the least n such that, no matter how n pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of pebbling moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. Let p1,p2,…,pn be positive integers and G be such a graph, V(G)=n. The thorn graph of the graph G, with parameters p1,p2,…,pn, is obtained by attaching pi new vertices of degree 1 to the vertex ui of the graph G, i=1,2,…,n. Graham conjectured that for any connected graphs G and H, f(G×H)≤f(G)f(H). We show that Graham’s conjecture holds true for a thorn graph of the complete graph with every by a graph with the two-pebbling property. As a corollary, Graham’s conjecture holds when G and H are the thorn graphs of the complete graphs with every . 相似文献
5.
W.A. Kirk 《Journal of Mathematical Analysis and Applications》2003,277(2):645-650
Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies
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If G is a connected graph with vertex set V, then the degree distance of G, D′(G), is defined as , where degw is the degree of vertex w, and d(u,v) denotes the distance between u and v. We prove the asymptotically sharp upper bound for graphs of order n and diameter d. As a corollary we obtain the bound for graphs of order n. This essentially proves a conjecture by Tomescu [I. Tomescu, Some extremal properties of the degree distance of a graph, Discrete Appl. Math. (98) (1999) 159-163]. 相似文献
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9.
J. Mc Laughlin 《Journal of Number Theory》2007,127(2):184-219
Let f(x)∈Z[x]. Set f0(x)=x and, for n?1, define fn(x)=f(fn−1(x)). We describe several infinite families of polynomials for which the infinite product
10.
In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))n?0 and (U(n))n?0, which are ultimately periodic modulo m, e.g.
11.
Jian-Hua Zheng 《Journal of Mathematical Analysis and Applications》2006,313(1):24-37
Let be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f(z) and proved, among others, that if f(z) has a Baker wandering domain U, then for all sufficiently large n, fn(U) contains a round annulus whose module tends to infinity as n→∞ and so for some 0<d<1,
12.
B.A.F. Wehrfritz 《Journal of Pure and Applied Algebra》2007,209(2):301-309
Let D be a division ring of finite degree d and let n be a positive integer. If G is any soluble subgroup of , we prove that G has derived length at most
9+log2d+(11/3)log2n 相似文献
13.
M. Anoussis 《Advances in Mathematics》2004,188(2):425-443
Let G be a compact group, not necessarily abelian, let ? be its unitary dual, and for f∈L1(G), let fn?f∗?∗f denote n-fold convolution of f with itself and f? the Fourier transform of f. In this paper, we derive the following spectral radius formula
14.
Yasuhito Miyamoto 《Journal of Differential Equations》2010,249(8):1853-1870
Let (n?3) be a ball, and let f∈C3. We are concerned with the Neumann problem
15.
Yasuo Teranishi 《Discrete Mathematics》2002,257(1):183-189
16.
A Roman domination function on a graph G=(V(G),E(G)) is a function f:V(G)→{0,1,2} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. The weight of a Roman dominating function is the value f(V(G))=∑u∈V(G)f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. Cockayne et al. [E. J. Cockayne et al. Roman domination in graphs, Discrete Mathematics 278 (2004) 11-22] showed that γ(G)≤γR(G)≤2γ(G) and defined a graph G to be Roman if γR(G)=2γ(G). In this article, the authors gave several classes of Roman graphs: P3k,P3k+2,C3k,C3k+2 for k≥1, Km,n for min{m,n}≠2, and any graph G with γ(G)=1; In this paper, we research on regular Roman graphs and prove that: (1) the circulant graphs and , n⁄≡1 (mod (2k+1)), (n≠2k) are Roman graphs, (2) the generalized Petersen graphs P(n,2k+1)( (mod 4) and ), P(n,1) (n⁄≡2 (mod 4)), P(n,3) ( (mod 4)) and P(11,3) are Roman graphs, and (3) the Cartesian product graphs are Roman graphs. 相似文献
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18.
Vladimir Nikiforov 《Linear algebra and its applications》2006,414(1):347-360
Let G be a graph with n vertices and m edges and let μ(G) = μ1(G) ? ? ? μn(G) be the eigenvalues of its adjacency matrix. Set s(G)=∑u∈V(G)∣d(u)-2m/n∣. We prove that
19.
Let G=(V,E) be a simple graph with vertex degrees d1,d2,…,dn. The Randi? index R(G) is equal to the sum over all edges (i,j)∈E of weights . We prove several conjectures, obtained by the system AutoGraphiX, relating R(G) and the chromatic number χ(G). The main result is χ(G)≤2R(G). To prove it, we also show that if v∈V is a vertex of minimum degree δ of G, G−v the graph obtained from G by deleting v and all incident edges, and Δ the maximum degree of G, then . 相似文献
20.
Toru Kojima 《Discrete Mathematics》2008,308(17):3770-3781
The bandwidth B(G) of a graph G is the minimum of the quantity max{|f(u)-f(v)|:uv∈E(G)} taken over all injective integer numberings f of G. The corona of two graphs G and H, written as G°H, is the graph obtained by taking one copy of G and |V(G)| copies of H, and then joining the ith vertex of G to every vertex in the ith copy of H. In this paper, we investigate the bandwidth of the corona of two graphs. For a graph G, we denote the connectivity of G by κ(G). Let G be a graph on n vertices with B(G)=κ(G)=k?2 and let H be a graph of order m. Let c,p and q be three integers satisfying 1?c?k-1 and . We define hi=(2k-1)m+(k-i)(⌊(2k-1)m/i⌋+1)+1 for i=1,2,…,k and b=max{⌈(n(m+1)-qm-1)/(p+2)⌉,⌈(n(m+1)+k-q-1)/(p+3)⌉}. Then, among other results, we prove that