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1.
The least eigenvalue of a connected graph is the least eigenvalue of its adjacency matrix. We characterize the connected graphs of order n and size n + k (5≤k≤8 and n>k + 5) with the minimal least eigenvalue. 相似文献
2.
We provide general existence criteria to solutions for a class of higher-order discrete boundary value problems. Our results supplement as well as improve several recent results established in the literature. 相似文献
3.
We study extremal graphs for the extremal values of the second largest Q-eigenvalue of a connected graph. We first characterize all simple connected graphs with second largest signless Laplacian eigenvalue at most 3. The second part of the present paper is devoted to the study of the graphs that maximize the second largest Q-eigenvalue. We construct families of such graphs and prove that some of theses families are minimal for the fact that they maximize the second largest signless Laplacian eigenvalue. 相似文献
4.
In this paper, we study the edge clique cover number of squares of graphs. More specifically, we study the inequality θ(G2)θ(G) where θ(G) is the edge clique cover number of a graph G. We show that any graph G with at most θ(G) vertices satisfies the inequality. Among the graphs with more than θ(G) vertices, we find some graphs violating the inequality and show that dually chordal graphs and power-chordal graphs satisfy the inequality. Especially, we give an exact formula computing θ(T2) for a tree T. 相似文献
5.
Hae-Soo Oh 《Topology and its Applications》1985,20(3)
In this paper we compute the Witt class of torsion linking forms of (4n−1)-dimensional closed oriented manifolds admitting orientation preserving pseudo-free circle actions. 相似文献
6.
Zhi-Wei Sun 《Combinatorica》2003,23(4):681-691
For a finite system
of arithmetic sequences
the covering function is w(x)
= |{1 s
k : x as (mod
ns)}|. Using equalities
involving roots of unity we characterize those systems with a
fixed covering function w(x). From the characterization we reveal
some connections between a period n0 of
w(x) and the moduli
n1, .
. . , nk in such a system
A. Here are three central
results: (a) For each r=0,1,
. . .,nk/(n0,nk)–1 there exists a
Jc{1, . . . ,
k–1} such that
. (b) If
n1
···nk–l <nk–l+1 =···=nk (0 <
l <
k), then for any positive
integer r <
nk/nk–l with
r 0 (mod
nk/(n0,nk)), the binomial
coefficient
can be written as the
sum of some (not necessarily distinct) prime divisors of
nk. (c)
max(xw(x)
can be written in the form
where
m1, .
. .,mk are positive
integers.The research is supported by the Teaching and
Research Award Fund for Outstanding Young Teachers in Higher
Education Institutions of MOE, and the National Natural Science
Foundation of P. R. China. 相似文献
7.
Given a graph G with characteristic polynomial ϕ(t), we consider the ML-decomposition ϕ(t) = q
1(t)q
2(t)2 ... q
m
(t)m, where each q
i
(t) is an integral polynomial and the roots of ϕ(t) with multiplicity j are exactly the roots of q
j
(t). We give an algorithm to construct the polynomials q
i
(t) and describe some relations of their coefficients with other combinatorial invariants of G. In particular, we get new bounds for the energy E(G) =
|λi| of G, where λ1, λ2, ..., λn are the eigenvalues of G (with multiplicity). Most of the results are proved for the more general situation of a Hermitian matrix whose characteristic
polynomial has integral coefficients.
This work was done during a visit of the second named author to UNAM. 相似文献
8.
Bin He Qing Meng Weiguo Rui Yao Long 《Communications in Nonlinear Science & Numerical Simulation》2008,13(10):2114-2123
Using the method of planar dynamical systems to the mK(n, n) equation, the existence of uncountably infinite many smooth and non-smooth periodic wave solutions, solitary wave solutions and kink and anti-kink wave solutions is proved. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All possible exact explicit parametric representations of smooth and non-smooth travelling wave solutions are obtain. 相似文献
9.
Consider the flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1. We prove that if is a nontrivial 2-(v, k, λ) symmetric design with (k, λ) = 1 and G≤Aut( ) is flag-transitive with Soc(G) = An for n≥5, then is the projective space PG2(3,2) and G = A7. 相似文献
10.
《Journal of Graph Theory》2018,88(1):222-231
A well‐known theorem of Gomory and Hu states that if G is a finite graph with nonnegative weights on its edges, then there exists a tree T (now called a Gomory‐Hu tree) on such that for all there is an such that the two components of determine an optimal (minimal valued) cut between u an v in G. In this article, we extend their result to infinite weighted graphs with finite total weight. Furthermore, we show by an example that one cannot omit the condition of the finiteness of the total weight. 相似文献
11.
V. A. Belonogov 《Siberian Mathematical Journal》2008,49(5):784-795
In studying the pairs of irreducible characters of the symmetric group S
n
with the same zero set on A
n
or S
n
∖ A
n
(as well as the pairs of irreducible characters with the same zero set on the alternating group A
n
), the results are important on the connection between the Young diagrams of the characters of these pairs. We prove a theorem
that considerably generalizes two previous results of frequent use in this direction.
Original Russian Text Copyright ? 2008 Belonogov V. A.
The author was supported by the Russian Foundation for Basic Research (Grant 07-01-00148) and the RFBR-NSFC (Grant 05-01-39000).
__________
Ekaterinburg. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 5, pp. 992–1006, September–October, 2008. 相似文献
12.
13.
14.
We prove that the contact graph of a 2-dimensional CAT(0) cube complex X of maximum degree Δ can be coloured with at most ?(Δ)=MΔ26 colours, for a fixed constant M. This implies that X (and the associated median graph) isometrically embeds in the Cartesian product of at most ?(Δ) trees, and that the event structure whose domain is X admits a nice labelling with ?(Δ) labels. On the other hand, we present an example of a 5-dimensional CAT(0) cube complex with uniformly bounded degrees of 0-cubes which cannot be embedded into a Cartesian product of a finite number of trees. This answers in the negative a question raised independently by F. Haglund, G. Niblo, M. Sageev, and the first author of this paper. 相似文献
15.
Michael Doob 《Linear algebra and its applications》2002,340(1-3):87-96
Circulant graphs satisfying det(−A(G))=−deg(G) are used to construct arbitrarily large families of graphs with determinant equal to that of the complete graph Kn. 相似文献
16.
Shang-wang Tan 《Discrete Mathematics》2010,310(5):1026-1212
The spectrum of weighted graphs is often used to solve the problems in the design of networks and electronic circuits. We first give some perturbational results on the (signless) Laplacian spectral radius of weighted graphs when some weights of edges are modified; we then determine the weighted tree with the largest Laplacian spectral radius in the set of all weighted trees with a fixed number of pendant vertices and a positive weight set. Furthermore, we also derive the weighted trees with the largest Laplacian spectral radius in the set of all weighted trees with a fixed positive weight set and independence number, matching number or total independence number. 相似文献
17.
Abbas Heydari 《Linear algebra and its applications》2008,429(7):1744-1757
Let H be a simple graph with n vertices and G be a sequence of n rooted graphs G1,G2,…,Gn. Godsil and McKay [C.D. Godsil, B.D. McKay, A new graph product and its spectrum, Bull. Austral. Math. Soc. 18 (1978) 21-28] defined the rooted product H(G), of H by G by identifying the root vertex of Gi with the ith vertex of H, and determined the characteristic polynomial of H(G). In this paper we prove a general result on the determinants of some special matrices and, as a corollary, determine the characteristic polynomials of adjacency and Laplacian matrices of H(G).Rojo and Soto [O. Rojo, R. Soto, The spectra of the adjacency matrix and Laplacian matrix for some balanced trees, Linear Algebra Appl. 403 (2005) 97-117] computed the characteristic polynomials and the spectrum of adjacency and Laplacian matrices of a class of balanced trees. As an application of our results, we obtain their conclusions by a simple method. 相似文献
18.
Jianqin Zhou 《Designs, Codes and Cryptography》2011,58(3):279-296
In this paper, we first optimize the structure of the Wei–Xiao–Chen algorithm for the linear complexity of sequences over GF(q) with period N = 2p
n
, where p and q are odd primes, and q is a primitive root modulo p
2. The second, an union cost is proposed, so that an efficient algorithm for computing the k-error linear complexity of a sequence with period 2p
n
over GF(q) is derived, where p and q are odd primes, and q is a primitive root modulo p
2. The third, we give a validity of the proposed algorithm, and also prove that there exists an error sequence e
N
, where the Hamming weight of e
N
is not greater than k, such that the linear complexity of (s + e)
N
reaches the k-error linear complexity c. We also present a numerical example to illustrate the algorithm. Finally, we present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. 相似文献
19.
Tams Lengyel 《Discrete Mathematics》1996,150(1-3):281-292
We partially characterize the rational numbers x and integers n 0 for which the sum ∑k=0∞ knxk assumes integers. We prove that if ∑k=0∞ knxk is an integer for x = 1 − a/b with a, b> 0 integers and gcd(a,b) = 1, then a = 1 or 2. Partial results and conjectures are given which indicate for which b and n it is an integer if a = 2. The proof is based on lower bounds on the multiplicities of factors of the Stirling number of the second kind, S(n,k). More specifically, we obtain
for all integers k, 2 k n, and a 3, provided a is odd or divisible by 4, where va(m) denotes the exponent of the highest power of a which divides m, for m and a> 1 integers.
New identities are also derived for the Stirling numbers, e.g., we show that ∑k=02nk! S(2n, k) , for all integers n 1. 相似文献
20.
M. A. Grechkoseeva 《Siberian Mathematical Journal》2007,48(1):73-75
We prove that the nonisomorphic simple groups B
n
(q) and C
n
(q) have different sets of element orders.
Original Russian Text Copyright ? 2007 Grechkoseeva M. A.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 1, pp. 89–92, January–February, 2007. 相似文献