共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
A graph is denoted by G with the vertex set V(G) and the edge set E(G). A path P = 〈v0, v1, … , vm〉 is a sequence of adjacent vertices. Two paths with equal length P1 = 〈 u1, u2, … , um〉 and P2 = 〈 v1, v2, … , vm〉 from a to b are independent if u1 = v1 = a, um = vm = b, and ui ≠ vi for 2 ? i ? m − 1. Paths with equal length from a to b are mutually independent if they are pairwisely independent. Let u and v be two distinct vertices of a bipartite graph G, and let l be a positive integer length, dG(u, v) ? l ? ∣V(G) − 1∣ with (l − dG(u, v)) being even. We say that the pair of vertices u, v is (m, l)-mutually independent bipanconnected if there exist m mutually independent paths with length l from u to v. In this paper, we explore yet another strong property of the hypercubes. We prove that every pair of vertices u and v in the n-dimensional hypercube, with dQn(u,v)?n-1, is (n − 1, l)-mutually independent bipanconnected for every with (l-dQn(u,v)) being even. As for dQn(u,v)?n-2, it is also (n − 1, l)-mutually independent bipanconnected if l?dQn(u,v)+2, and is only (l, l)-mutually independent bipanconnected if l=dQn(u,v). 相似文献
3.
Vladimir Nikiforov 《Linear algebra and its applications》2007,422(1):284-290
Suppose a graph G have n vertices, m edges, and t triangles. Letting λn(G) be the largest eigenvalue of the Laplacian of G and μn(G) be the smallest eigenvalue of its adjacency matrix, we prove that
4.
In this paper, we show that, for every locally compact abelian group G, the following statements are equivalent:
- (i)
- G contains no sequence such that {0}∪{±xn∣n∈N} is infinite and quasi-convex in G, and xn?0;
- (ii)
- one of the subgroups {g∈G∣2g=0} or {g∈G∣3g=0} is open in G;
- (iii)
- G contains an open compact subgroup of the form or for some cardinal κ.
5.
Let G be a graph with n vertices and m edges. Let λ1, λ2, … , λn be the eigenvalues of the adjacency matrix of G, and let μ1, μ2, … , μn be the eigenvalues of the Laplacian matrix of G. An earlier much studied quantity is the energy of the graph G. We now define and investigate the Laplacian energy as . There is a great deal of analogy between the properties of E(G) and LE(G), but also some significant differences. 相似文献
6.
7.
Let 1 ? p ? ∞, 0 < q ? p, and A = (an,k)n,k?0 ? 0. Denote by Lp,q(A) the supremum of those L satisfying the following inequality:
8.
Kinkar Ch. Das 《Linear algebra and its applications》2011,435(10):2420-2424
Let G = (V, E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the signless Laplacian matrix of G is Q(G) = D(G) + A(G). In [5], Cvetkovi? et al. have given the following conjecture involving the second largest signless Laplacian eigenvalue (q2) and the index (λ1) of graph G (see also Aouchiche and Hansen [1]):
9.
10.
Yevhen Zelenyuk 《Journal of Combinatorial Theory, Series A》2008,115(2):331-339
Let G be an Abelian group and let be infinite. We construct a partition of A such that whenever (xn)n<ω is a one-to-one sequence in A, g∈G and m<ω, one has
(g+FSI((xn)n<ω))∩Am≠∅, 相似文献
11.
A.R. Rao 《Discrete Mathematics》2006,306(14):1595-1600
For a digraph G, let R(G) (respectively, R(k)(G)) be the number of ordered pairs (u,v) of vertices of G such that u≠v and v is reachable from u (respectively, reachable from u by a path of length ?k). In this paper, we study the range Sn of R(G) and the range of R(k)(G) as G varies over all possible digraphs on n vertices. We give a sufficient condition and a necessary condition for an integer to belong to Sn. These determine the set Sn for all n?208. We also determine for k?4 and show that whenever n?k+(k+1)0.57+2, for arbitrary k. 相似文献
12.
Vladimir Nikiforov 《Linear algebra and its applications》2008,428(7):1492-1498
Let G be a graph of sufficiently large order n, and let the largest eigenvalue μ(G) of its adjacency matrix satisfies . Then G contains a cycle of length t for every t?n/320This condition is sharp: the complete bipartite graph T2(n) with parts of size ⌊n/2⌋ and ⌈n/2⌉ contains no odd cycles and its largest eigenvalue is equal to .This condition is stable: if μ(G) is close to and G fails to contain a cycle of length t for some t?n/321, then G resembles T2(n). 相似文献
13.
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.
14.
15.
16.
We find lower bounds on the difference between the spectral radius λ1 and the average degree of an irregular graph G of order n and size e. In particular, we show that, if n ? 4, then
17.
Martin Klazar 《Journal of Number Theory》2007,124(2):470-490
Let m(n) be the number of ordered factorizations of n?1 in factors larger than 1. We prove that for every ε>0
18.
Linghai Zhang 《Journal of Differential Equations》2008,245(11):3470-3502
Let u=u(x,t,u0) represent the global strong/weak solutions of the Cauchy problems for the general n-dimensional incompressible Navier-Stokes equations
19.
20.