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1.
Crossing numbers of graphs are in general very difficult to compute. There are several known exact results on the crossing
number of the Cartesian products of paths, cycles or stars with small graphs. In this paper we study cr(Km □ Pn), the crossing number of the Cartesian product Km □ Pn. We prove that
for m ≥ 3,n ≥ 1 and cr(Km □ Pn)≥ (n − 1)cr(Km+2 − e) + 2cr(Km+1). For m≤ 5, according to Klešč, Jendrol and Ščerbová, the equality holds. In this paper, we also prove that the equality holds for
m = 6, i.e., cr(K6 □ Pn) = 15n + 3.
Research supported by NFSC (60373096, 60573022). 相似文献
2.
In this paper, the structure of the critical group of the graph K
m
× C
n
is determined, where m, n ≥ 3. 相似文献
3.
The minimum number of total independent partition sets of V ∪ E of graph G(V,E) is called the total chromatic number of G denoted by χ
t
(G). If the difference of the numbers of any two total independent partition sets of V ∪ E is no more than one, then the minimum number of total independent partition sets of V ∪ E is called the equitable total chromatic number of G, denoted by χ
et
(G). In this paper, we obtain the equitable total chromatic number of the join graph of fan and wheel with the same order.
Supported by the National Natural Science Foundation of China (No. 10771091). 相似文献
4.
In this paper, we show that, for each p 〉 1, there are continuum many Borel equivalence relations between Rω/l1 and Rω/p ordered by ≤B which are pairwise Borel incomparable. 相似文献
5.
This paper is concerned with the study of the set P
-1(0), when P varies over all orthogonally additive polynomials on
p
and L
p
spaces. We apply our results to obtain characterizations of the weak-polynomial topologies associated to this class of polynomials. 相似文献
6.
We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs (constructed in [LPS]). They are obtained as quotients of the buildings of typeà d?1 associated with PGL d (F) whereF is a local field of positive characteristic. 相似文献
7.
Emília Draženská 《Mathematica Slovaca》2011,61(5):675-686
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. The
crossing numbers of G□C
n
for some graphs G on five and six vertices and the cycle C
n
are also given. In this paper, we extend these results by determining the crossing number of the Cartesian product G □ C
n
, where G is a specific graph on six vertices. 相似文献
8.
The set of all non-increasing nonnegative integer sequences π = (d(v
1), d(v
2), …, d(v
n
)) is denoted by NS
n
. A sequence π ∈ NS
n
is said to be graphic if it is the degree sequence of a simple graph G on n vertices, and such a graph G is called a realization of π. The set of all graphic sequences in NS
n
is denoted by GS
n
. A graphical sequence π is potentially H-graphical if there is a realization of π containing H as a subgraph, while π is forcibly H-graphical if every realization of π contains H as a subgraph. Let K
k
denote a complete graph on k vertices. Let K
m
−H be the graph obtained from Km by removing the edges set E(H) of the graph H (H is a subgraph of K
m
). This paper summarizes briefly some recent results on potentially K
m
−G-graphic sequences and give a useful classification for determining σ (H, n). 相似文献
9.
Yu. K. Dem’yanovich 《Journal of Mathematical Sciences》2009,156(4):577-588
A general approach to the construction of asymptotics of coordinate (not necessarily polynomial) B
φ
-splines of an arbitrary order is proposed. Asymptotic representations for Lagrange type third order B
φ
-splines are obtained. Bibliography: 4 titles.
Translated from Problemy Matematicheskogo Analiza, No. 38, December 2008, pp. 11–21. 相似文献
10.
Sh. M. Nasibov 《Mathematical Notes》2017,101(1-2):123-131
Sufficient conditions for the blow-up of nontrivial generalized solutions of the interior Dirichlet problem with homogeneous boundary condition for the homogeneous elliptic-type equation Δu + q(x)u = 0, where either q(x) ≠ const or q(x) = const= λ > 0, are obtained. A priori upper bounds (Theorem 4 and Remark 6) for the exact constants in the well-known Sobolev and Steklov inequalities are established. 相似文献
11.
Kenji Kamizono 《Proceedings of the Steklov Institute of Mathematics》2009,265(1):115-130
In this paper, we generalize the result of Bikulov and Volovich (1997) and construct a p-adic Brownian motion over ℚ
p
. First, we construct directly a p-adic white noise over ℚ
p
by using a specific complete orthonormal system of (ℚ
p
). A p-adic Brownian motion over ℚ
p
is then constructed by the Paley-Wiener method. Finally, we introduce a p-adic random walk and prove a theorem on the approximation of a p-adic Brownian motion by a p-adic random walk. 相似文献
12.
Based on the prime graph of a finite simple group, its order is the product of its order components (see [4]). We prove that the simple groups PSU3(q) are uniquely determined by their order components. Our result immediately implies that the Thompsons conjecture and the Wujie Shis conjecture [16] are valid for these groups.AMS Subject Classification: 20D05, 20D60 相似文献
13.
R. Słowik 《印度理论与应用数学杂志》2017,48(3):323-334
We prove that if F is a field such that |F| > 2, then every bilocal automorphism of T ∞(F) - the algebra of ? × ? upper triangular matrices over F, is an automorphism. 相似文献
14.
We investigate the relation between analytic Campanato spaces \(\mathcal {AL}_{p,s}\) and the spaces F(p, q, s), characterize the bounded and compact Riemann–Stieltjes operators from \(\mathcal {AL}_{p,s}\) to \(F(p,p-s-1,s)\). We also describe the corona theorem and the interpolating sequences for the class \(F(p,p-2,s)\), which is the Möbius invariant subspace of the analytic Besov type spaces \(B_p(s)\). 相似文献
15.
We use the method of local representation and original method of Brauer to study the block with K(B)−L(B)=1, and get some properties on the defect group and the structure of this kind of blocks. Then, we show that K(B) conjecture holds for this kind of blocks. 相似文献
16.
Joachim Breitner 《Israel Journal of Mathematics》2012,191(2):545-557
For a representative class of subgroups of F r , the image of their stabilizer subgroup under the action of Aut(F r ) in GL r (ℤ) is calculated. 相似文献
17.
In this paper we give a characterization of the pointwise multipliers of the holomorphic Triebel-Lizorkin spaces F, qs, and we apply these results to prove a corona decomposition theorem for these spaces.Mathematics Subject Classification (1991):32A37Both authors partially supported by DGICYT Grant BMF2002-04072-C02-01 and CIRIT Grant 2001-SGR-00172 相似文献
18.
The article presents new results on convergence in L p ([0,T]) of wavelet expansions of φ-sub-Gaussian random processes. The convergence rate of the expansions is obtained. Specifications of the obtained results are discussed. 相似文献
19.
Akira Hiraki 《Graphs and Combinatorics》2009,25(1):65-79
Let Γ be a distance-regular graph of diameter d ≥ 3 with c
2 > 1. Let m be an integer with 1 ≤ m ≤ d − 1. We consider the following conditions:
In [12] we have shown that the condition (SC)
m
holds if and only if both of the conditions (BB)
i
and (CA)
i
hold for i = 1,...,m. In this paper we show that if a
1 = 0 < a
2 and the condition (BB)
i
holds for i = 1,...,m, then the condition (CA)
i
holds for i = 1,...,m. In particular, the condition (SC)
m
holds. Applying this result we prove that a distance-regular graph with classical parameters (d, b, α, β) such that c
2 > 1 and a
1 = 0 < a
2 satisfies the condition (SC)
i
for i = 1,...,d − 1. In particular, either (b, α, β) = (− 2, −3, −1 − (−2)
d
) or holds. 相似文献
(SC) m : For any pair of vertices at distance m there exists a strongly closed subgraph of diameter m containing them. | |
(BB) m : Let (x, y, z) be a triple of vertices with ∂Γ(x, y) = 1 and ∂Γ(x, z) = ∂Γ(y, z) = m. Then B(x, z) = B(y, z). | |
(CA) m : Let (x, y, z) be a triple of vertices with and |C(z, x) ∩ C(z, y)| ≥ 2. Then C(x, z) ∪ A(x, z) = C(y, z) ∪ A(y, z). |
20.
We show, conditional on a uniform version of the prime k-tuples conjecture, that there are x/(log x)1+o(1) numbers not exceeding x common to the ranges of φ and σ. Here φ is Euler’s totient function and σ is the sum-of-divisors function. 相似文献