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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.
We construct a class of modules for the twisted multi-loop algebra of type A 1×A 1 by applying Wakimoto free bosonic realization. We also discuss the structures and the irreducibility of the Fock space. 相似文献
5.
V. D. Lyakhovsky 《Journal of Mathematical Sciences》2008,151(2):2907-2923
New solutions of twist equations for the universal enveloping algebras U (An−1) are found. These solutions can be represented as products of full chains of extended Jordanian twists Abelian factors (“rotations”) , and sets of quasi-Jordanian twists . The latter are generalizations of Jordanian twists (with carrier b2) for special deformed extensions of the Hopf algebra U (b2). The carrier subalgebra for the composition is a nonminimal parabolic subalgebra in A
n−1 such that . The parabolic twisting elements are obtained in an explicit form. Details of the construction are illustrated by considering the examples n = 4 and n = 11.
Bibliography: 21 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 187–213. 相似文献
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
Let an algebraic curve f have a singular point of type Aμ or Dμ. Let
be the curve obtained by smoothing the singular point of f. In this paper, local maximal meanders appearing under an M-smoothing
in a neighborhood of the singular point are studied. A local maximal meander means that the number of real points of the intersection
of
with a coordinate axis in the neighborhood is maximal and the points belong to one of the components of
. An M-smoothing means that the number of components of
which appear in the neighborhood under the smoothing is also maximal. Bibliography: 9 titles.
__________
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 193–217. 相似文献
13.
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
14.
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
15.
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
16.
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
17.
This paper deals with subrings of the type of a domain T of type where D is a domain and is a nonzero prime ideal of T, generalizing the classical A + M construction. We examine the possible transfer of the universal catenarity from A and T to R. This study allows us to generalize and improve some known results and to provide several interesting applications and examples.
相似文献
18.
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
19.
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
20.
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). |