图G为自构线图的充要条件

首次给出自构线图的定义,并证明:简单图G为自构线图的充要条件是图G为2-正则简单图.     

The Spectrum and Automorphism Group of the Set-Inclusion Graph

Let n,k and l be integers with 1 ≤ k ＜ l ≤ n-1.The set-inclusion graph G(n,k,l) is the graph whose vertex set consists of all k-andl-subsets of[n]={1,2,...,n},where two distinct vertices are adjacent if one of them is contained in the other.In this paper,we determine the spectrum and automorphism group of G(n,k,l).     

An Ergodic Action of the Outer Automorphism Group of a Free Group

For n > 2, the action of the outer automorphism group of the rank n free group F _n on Hom(F _n , SU(2))/SU(2) is ergodic with respect to the Lebesgue measure class. The author gratefully acknowledges support from National Science Foundation grants DMS-0405605 and DMS-0103889. Received: September 2005 Revision: January 2006 Accepted: March 2006     

The Semi-Arc Automorphism Group of a Graph with Application to Map Enumeration

A map is a connected topological graph cellularly embedded in a surface. For a given graph Γ, its genus distribution of rooted maps and embeddings on orientable and non-orientable surfaces are separately investigated by many researchers. By introducing the concept of a semi-arc automorphism group of a graph and classifying all its embeddings under the action of its semi-arc automorphism group, we find the relations between its genus distribution of rooted maps and genus distribution of embeddings on orientable and non-orientable surfaces, and give some new formulas for the number of rooted maps on a given orientable surface with underlying graph a bouquet of cycles B_n, a closed-end ladder L_n or a Ringel ladder R_n. A general scheme for enumerating unrooted maps on surfaces(orientable or non-orientable) with a given underlying graph is established. Using this scheme, we obtained the closed formulas for the numbers of non-isomorphic maps on orientable or non-orientable surfaces with an underlying bouquet B_n in this paper.     

On the Stabilizer of the Automorphism Group of a 4—valent Vertex—transitive Graph with Odd—prime—power Order

Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p^κ（κ≥1） and let A be the full automorphism group of X.In this paper,we prove that the stabilizer Av of a vertex v in A is a 2-group if p≠5,or a {2,3}-group if p=5.Furthermore,if p=5|Av| is not divisible by 3^2.As a result ,we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p^κ(κ≥1） is at most 1-arc-transitive for p≠5 and 2-arc-transitive for p=5.     

Determination of a Domain in Complex Space by its Automorphism Group

We consider results, both in one complex variable and several, which show that the algebraic or geometric structure of the automorphism group of a domain z can determine that domain. The domains considered include Ω = B, the unit ball in C ⁿ , and Ω = C ⁿ . Various illustrative examples are provided.     

Integer Functions on the Cycle Space and Edges of a Graph

A directed graph has a natural \mathbb Z{\mathbb {Z}} -module homomorphism from the underlying graph’s cycle space to \mathbb Z{\mathbb {Z}} where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any \mathbb Z{\mathbb {Z}} -module homomorphism of a graph’s cycle space to \mathbb Z{\mathbb {Z}} that satisfies these two properties for all cycles must be such a map induced from an edge direction on the graph. In this paper we will prove a generalization of this theorem and an analogue as well.     

Subspace Inclusion Graph of a Vector Space

In this paper, the authors introduce a graph structure, called subspace inclusion graph ?n(𝕍) on a finite dimensional vector space 𝕍 where the vertex set is the collection of nontrivial proper subspaces of a vector space and two vertices are adjacent if one is contained in other. The diameter, girth, clique number, and chromatic number of ?n(𝕍) are studied. It is shown that two subspace inclusion graphs are isomorphic if and only if the base vector spaces are isomorphic. Finally, some properties of subspace inclusion graph are studied when the base field is finite.     

Long Cycles Generate the Cycle Space of a Graph

Let G be a 2-connected graph in which the degree of every vertex is at least d. We prove that the cycles of length at least d + 1 generate the cycle space of G, unless G ≌ K_d+1 and d is odd. As a corollary, we deduce that the cycles of length at least d + 1 generate the subspace of even cycles in G. We also establish the existence of odd cycles of length at least d + 1 in the case when G is not bipartite.A second result states: if G is 2-connected with chromatic number at least k, then the cycles of length at least k generate the cycle space of G, unless G ≌ K_k and k is even. Similar corollaries follow, among them a stronger version of a theorem of Erdös and Hajnal.     

Automorphism Group of the Rank-decreasing Graph Over the Semigroup of Upper Triangular Matrices

Let F_q be a finite field with q elements, n ≥ 2 a positive integer, and T(n, q) the semigroup of all n × n upper triangular matrices over F_q. The rank-decreasing graph 𝕋 of T(n, q) is a directed graph which has T(n, q) as vertex set, and there is a directed edge from A ∈ T(n, q) to B ∈ T(n, q) if and only if r(AB) < r(B). The zero-divisor graph 𝒯 of T(n, q), with vertex set of all nonzero zero-divisors of T(n, q) and there is a directed edge from a vertex A to a vertex B if and only if AB = 0, can be viewed as a subgraph of 𝕋. In [16 Wang, L. (2015). A note on automorphisms of the zero-divisor graph of upper triangular matrices. Lin. Alg. Appl. 465:214–220.[Crossref], [Web of Science ®] , [Google Scholar]], L. Wang has determined the automorphisms of the zero-divisor graph 𝒯 of T(n, q). In this article, by applying the main result of [17 Wong, D., Ma, X., Zhou, J. (2014). The group of automorphisms of a zero-divisor graph based on rank one upper triangular matrices. Lin. Alg. Appl. 460:242–258.[Crossref], [Web of Science ®] , [Google Scholar]] we determine the automorphisms of the rank-decreasing graph 𝕋 of T(n, q).     

Space of Ricci Flows I

In this paper, we study the moduli spaces of m‐dimensional, κ‐noncollapsed Ricci flow solutions with bounded $\int |Rm|^{{m}/{2}}$ and bounded scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study the estimates of isoperimetric constants, the Kähler‐Ricci flows, and the moduli spaces of gradient shrinking solitons. © 2012 Wiley Periodicals, Inc.     

The Automorphism Group and the Convex Subgraphs of the Quadratic Forms Graph in Characteristic 2

We determine the automorphism group and the convex subgraphs of the quadratic forms graph Quad(n,q),q even.A. Munemasa: A part of this research was completed during this author's visit at the Institute for System Analysis, Moscow, as a Heizaemon Honda fellow of the Japan Association for Mathematical SciencesD.V. Pasechnik: A part of this research was completed when this author held a position at the Institute for System Analysis, MoscowS.V. Shpectorov: A part of this research was completed during this author's visit at the University of Technology, Eindhoven     

Nonzero Component Graph of a Finite Dimensional Vector Space

In this article, we introduce a graph structure, called a nonzero component graph on finite dimensional vector spaces. We show that the graph is connected and find its domination number and independence number. We also study the inter-relationship between vector space isomorphisms and graph isomorphisms, and it is shown that two graphs are isomorphic if and only if the corresponding vector spaces are so. Finally, we determine the degree of each vertex in case the base field is finite.     

Correction to the Paper - Determination of a Domain in Complex Space by its Automorphism Group

The author offers some corrections to his article which appeared in Vol. 47, No. 3 of this journal.     

Coloring the Vertices of a Graph With Measurable Sets in a Probability Space

We introduce a class of “chromatic” graph parameters that include the chromatic number, the circular chromatic number, the fractional chromatic number, and an uncountable horde of others. We prove some basic results about this class and pose some problems.     

非拟本原（PSU3（P），2）-弧传递图的外自同构

证明由GF（p^2）的域自同构可以产生一类非拟本原（PSU3（P），2）-弧传递图的白同构，并研究了这样的自同构与图的传递自同构群中心化予的关系。     

Adjoint Action of Automorphism Groups on Radical Endomorphisms,Generic Equivalence and Dynkin Quivers

Let Q be a connected quiver with no oriented cycles, k the field of complex numbers and P a projective representation of Q. We study the adjoint action of the automorphism group Aut _kQ P on the space of radical endomorphisms radEnd _kQ P. Using generic equivalence, we show that the quiver Q has the property that there exists a dense open Aut _kQ P-orbit in radEnd _kQ P, for all projective representations P, if and only if Q is a Dynkin quiver. This gives a new characterisation of Dynkin quivers.     

Viscous Flows in a Half Space Caused by Tangential Vibrations on Its Boundary

The paper is devoted to the studies of viscous flows caused by a vibrating boundary. The fluid domain is a half‐space, its boundary is a nondeformable plane that exhibits purely tangential vibrations. Such a simple geometrical setting allows us to study general boundary velocity fields and to obtain general results. From a practical viewpoint, such boundary conditions may be seen as the tangential vibrations of the material points of a stretchable plane membrane. In contrast to the classical boundary layer theory, we aim to build a global solution. To achieve this goal we employ the Vishik–Lyusternik approach, combined with two‐timing and averaging methods. Our main result is: we obtain a uniformly valid in the whole fluid domain approximation to the global solutions. This solution corresponds to general boundary conditions and to three different settings of the main small parameter. Our solution always include the inner part and outer part that both contain oscillating and non‐oscillating components. It is shown that the nonoscillating outer part of the solution is governed either by the full Navier–Stokes equations or the Stokes equations (both with the unit viscosity) and can be interpreted as a steady or unsteady streaming. In contrast to the existing theories of a steady streaming, our solutions do not contain any secular (infinitely growing with the inner normal coordinate) terms. The examples of the spatially periodic vibrations of the boundary and the angular torsional vibrations of an infinite rigid disc are considered. These examples are still brief and illustrative, while the core of the paper is devoted to the adaptation of the Vishik–Lyusternik method to the development of the general theory of vibrational boundary layers.