小Excess与具负下界Ricci曲率开流形的拓扑

In this paper,we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry.We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius,which improves some results in [4].     

Tetravalent edge-transitive graphs of order p 2 q

A graph is called edge-transitive if its full automorphism group acts transitively on its edge set.In this paper,by using classification of finite simple groups,we classify tetravalent edge-transitive graphs of order p2q with p,q distinct odd primes.The result generalizes certain previous results.In particular,it shows that such graphs are normal Cayley graphs with only a few exceptions of small orders.     

Isomorphisms of finite semi-Cayley graphs

Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph(Cayley isomorphism) if its isomorphic images are induced by automorphisms of G. A well-known result of Babai states that a Cayley graph Γ of G is a CI-graph if and only if all regular subgroups of Aut(Γ) isomorphic to G are conjugate in Aut(Γ). A semi-Cayley graph(also called bi-Cayley graph by some authors) over G is a simple graph whose automorphism group has a semiregular subgroup isomorphic to G with two orbits(of equal size). In this paper, we introduce the concept of SCI-graph(semi-Cayley isomorphism)and prove a Babai type theorem for semi-Cayley graphs. We prove that every semi-Cayley graph of a finite group G is an SCI-graph if and only if G is cyclic of order 3. Also, we study the isomorphism problem of a special class of semi-Cayley graphs.     

Recognizing Finite Groups Through Order and Degree Patterns

The degree pattern of a finite group G associated with its prime graph has been introduced by Moghaddamfar in 2005 and it is proved that the following simple groups are uniquely determined by their order and degree patterns:All sporadic simple groups,the alternating groups Ap(p≥5 is a twin prime)and some simple groups of the Lie type.In this paper,the authors continue this investigation.In particular,the authors show that the symmetric groups Sp+3,where p+2 is a composite number and p+4 is a prime and 97相似文献   

On Compact Graphs

Let G be a finite simple graph with adjacency matrix A, and let P（A） be the convex closure of the set of all permutation matrices commuting with A. G is said to be compact if every doubly stochastic matrix which commutes with A is in P（A）. In this paper, we characterize 3-regular compact graphs and prove that if G is a connected regular compact graph, G - v is also compact, and give a family of almost regular compact connected graphs.     

On Tame Kernels and Ideal Class Groups

It is well known that there is a close connection between tame kernels and ideal class groups of number fields. However, the latter is a very difficult subject in number theory. In this paper, we prove some results connecting the p^n-rank of the tame kernel of a cyclic cubic field F with the p^n-rank of the coinvariants of μp^n×CI（δE,T） under the action of the Galois group, where E = F（ζp^n ） and T is the finite set of primes of E consisting of the infinite primes and the finite primes dividing p. In particular, if F is a cyclic cubic field with only one ramified prime and p = 3, n = 2, we apply the results of the tame kernels to prove some results of the ideal class groups of E, the maximal real subfield of E and F（ζ3）.     

利用GAP研究一般线性群的抛物子群

A typical example for the algebraic groups is the general linear groups G = GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups.For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.     

THE NORMALITY OF ALGEBROID MULTIFUNCTIONS AND THEIR COEFFICIENT FUNCTIONS

In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent to their coefficient functions in some conditions.Furthermore, we obtain some new normality criteria for algebroid multifunctions families based on these results. We also provide some examples to expound that some restricted conditions of our main results are necessary.     

Simple zero property of some holomorphic functions on the moduli space of tori

We prove that some holomorphic functions on the moduli space of tori have only simple zeros.Instead of computing the derivative with respect to the moduli parameter τ, we introduce a conceptual proof by applying Painlevé Ⅵ equation. As an application of this simple zero property, we obtain the smoothness of the degeneracy curves of trivial critical points for some multiple Green function.     

Locally Transitive Graphs Admitting a Group with Cyclic Sylow Subgroups

All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.     

Laplacian Spectrum of Non-Commuting Graphs of Finite Groups

In this paper, we compute the Laplacian spectrum of non-commuting graphs of some classes of finite non-abelian groups. Our computations reveal that the non-commuting graphs of all the groups considered in this paper are L-integral. We also obtain some conditions on a group so that its non-commuting graph is L-integral.     

图的中间图2-pebbling性质和Graham猜想

本文研究了图的2-pebbling性质和Graham猜想.利用图的pebbling数的一些结果,我们研究了路和圈的中间图具有2-pebbling性质,从而也证明了路的中间图满足Graham猜想.     

完全$r$部图乘积上的Graham猜想

图G的Pebbling数f(G)是最小的正整数n,使得不论n个Pebble如何放置在G的顶点上,总可以通过一系列的Pebbling移动把1个Pebble移到任意一点上,其中Pebbling移动是从一个顶点处移走两个Pebble而把其中一个移到与其相邻的一个顶点上.Graham猜测对于任意的连通图G和H有f(G×H)≤f(G)f(H).本文证明对于一个完全γ部图和一个具有2-Pebbleing性质的图来说,Graham猜想成立.作为一个推论,当G和H均为完全γ部图时,Graham猜想成立.     

ALPERIN'S CONJECTURE FOR ALGEBRAIC GROUPS

We prove analogues for reductive algebraic groups of some resultsfor finite groups due to Knörr and Robinson from ‘Someremarks on a conjecture of Alperin’, J. London Math. Soc(2) 39 (1989), 48–60, which play a central rôlein their reformulation of Alperin's conjecture for finite groups.     

关于商高数的Jemanowicz猜想

本文研究了商高数的Jemanowicz猜想的整数解问题.利用初等数论方法,获得了该猜想的两个新结果并给出证明,推广了文献[4–8]的结果.     

On Symmetric Cayley Graphs of Valency Eleven

A Cayley graph Γ=Cay(G,S)is said to be normal if G is normal in Aut Γ.In this paper,we investigate the normality problem of the connected 11-valent symmetric Cayley graphs Γ of finite nonabelian simple groups G,where the vertex stabilizer Av is soluble for A=Aut Γ and v ∈ VΓ.We prove that either Γ is normal or G=A5,A10,A54,A274,A549 or A1099.Further,11-valent symmetric nonnormal Cayley graphs of A5,A54 and A274 are constructed.This provides some more examples of nonnormal 11-valent symmetric Cayley graphs of finite nonabelian simple groups after the first graph of this kind(of valency 11)was constructed by Fang,Ma and Wang in 2011.     

On Spectra of Almost Simple Extensions of Even-Dimensional Orthogonal Groups

The spectrum of a finite group is the set of the orders of its elements. We consider the problem that arises within the framework of recognition of finite simple groups by spectrum: Determine all finite almost simple groups having the same spectrum as its socle. This problem was solved for all almost simple groups with exception of the case that the socle is a simple even-dimensional orthogonal group over a field of odd characteristic. Here we address this remaining case and determine the almost simple groups in question.Also we prove that there are infinitely many pairwise nonisomorphic finite groups having the same spectrum as the simple 8-dimensional symplectic group over a field of characteristic other than 7.     

Oriented bipartite graphs and the Goldbach graph

In this paper, we study oriented bipartite graphs. In particular, we introduce “bitransitive” graphs. Several characterizations of bitransitive bitournaments are obtained. We show that bitransitive bitounaments are equivalent to acyclic bitournaments. As applications, we characterize acyclic bitournaments with Hamiltonian paths, determine the number of non-isomorphic acyclic bitournaments of a given order, and solve the graph-isomorphism problem in linear time for acyclic bitournaments. Next, we prove the well-known Caccetta-Häggkvist Conjecture for oriented bipartite graphs in some cases for which it is unsolved, in general, for oriented graphs. We also introduce the concept of undirected as well as oriented “odd-even” graphs. We characterize bipartite graphs and acyclic oriented bipartite graphs in terms of them. In fact, we show that any bipartite graph (acyclic oriented bipartite graph) can be represented by some odd-even graph (oriented odd-even graph). We obtain some conditions for connectedness of odd-even graphs. This study of odd-even graphs and their connectedness is motivated by a special family of odd-even graphs which we call “Goldbach graphs”. We show that the famous Goldbach's conjecture is equivalent to the connectedness of Goldbach graphs. Several other number theoretic conjectures (e.g., the twin prime conjecture) are related to various parameters of Goldbach graphs, motivating us to study the nature of vertex-degrees and independent sets of these graphs. Finally, we observe Hamiltonian properties of some odd-even graphs related to Goldbach graphs for a small number of vertices.     

Altermatic number of categorical product of graphs

In this paper, we prove some relaxations of Hedetniemi’s conjecture in terms of altermatic number and strong altermatic number of graphs, two combinatorial parameters introduced by the present authors Alishahi and Hajiabolhassan (2015) providing two sharp lower bounds for the chromatic number of graphs. In terms of these parameters, we also introduce some sharp lower bounds for the chromatic number of the categorical product of two graphs. Using these lower bounds, we present some new families of graphs supporting Hedetniemi’s conjecture.     

An Algebraic Formulation of the Graph Reconstruction Conjecture

The graph reconstruction conjecture asserts that every finite simple graph on at least three vertices can be reconstructed up to isomorphism from its deck—the collection of its vertex‐deleted subgraphs. Kocay's Lemma is an important tool in graph reconstruction. Roughly speaking, given the deck of a graph G and any finite sequence of graphs, it gives a linear constraint that every reconstruction of G must satisfy. Let be the number of distinct (mutually nonisomorphic) graphs on n vertices, and let be the number of distinct decks that can be constructed from these graphs. Then the difference measures how many graphs cannot be reconstructed from their decks. In particular, the graph reconstruction conjecture is true for n‐vertex graphs if and only if . We give a framework based on Kocay's lemma to study this discrepancy. We prove that if M is a matrix of covering numbers of graphs by sequences of graphs, then . In particular, all n‐vertex graphs are reconstructible if one such matrix has rank . To complement this result, we prove that it is possible to choose a family of sequences of graphs such that the corresponding matrix M of covering numbers satisfies .