消去图、覆盖图和均匀图的若干结果

设 G是一个图 ,g,f是定义在图 G的顶点集上的两个整数值函数 ,且g≤f.图 G的一个 ( g,f) -因子是 G的一个支撑子图 F,使对任意的 x∈V( F)有g( x)≤ d F( x)≤ f ( x) .文中推广了 ( g,f) -消去图、( g,f ) -覆盖图和 ( g,f) -均匀图的概念 ,给出了在 g相似文献   

书本图Bm的协调和相继标号

本文给出了书本图Ｂ２ｍ的ｍ种不同的相继标号和Ｂ４ｍ＋１的ｍ种不同的相继标号。因而，书本图Ｂｍ是相继图的充分条件为：ｍ＞１且ｍ≠（３ｍｏｄ４）。这一条件也是书本图Ｂｍ是协调图的充要条件。     

（mg＋m—1,mf—m＋1）—图的（g,f）—因子

本文证明了（ｍｇ＋ｍ－１,ｍｆ－ｍ＋１）－图具有一些特殊的（ｇ,ｆ）－因子,从而推广到了关于（ｇ,ｆ）－覆盖图和（ｇ,ｆ）－消去图的有关结果,有助于进一步研究（ｍｇ＋ｍ－１,ｍｆ－ｍ＋１）－图的正交因子分解问题。     

两类满足A（H）=3的图

本文利用文[3]的方法给出了两类满足A(H)=3的图,从而肯定了满足A(H)=3的图是不唯一的。本文还给出了满足A(H)=3的最小图。     

Hamilton图的特定生成了图问题的反例

［１］定理３断言：一个Ｈａｍｉｌｔｏｎ图Ｇ必存在仅有ｐ条桥的相间偶圈，如果相间偶圈的边中有边在Ｇ的ｐ个不连通初等子圈上（ｐ≥２）。本的反例表明上述结论是错的，从而［１］中关于Ｐｅｔｅｒｓｏｎ图不是Ｈａｍｉｌｔｏｎ图的证明也不成立。     

(g,f)-消去图的若干充分条件

设 G是一个图 ,用 V(G)和 E(G)表示它的顶点集和边集 ,并设 g和 f是定义在 V(G)上的两个整数值函数且 g 相似文献   

（a,b,k）—临界图

设Ｇ是一个图且设ａ，ｂ是非负整数，ａ〈ｂ。如果消去Ｇ的任意ｋ个顶点剩下的图有〔ａ，ｂ〕因子，则称图Ｇ是（ａ，ｂ，ｋ）－临界图。本文给出了一个图是（ａ，ｂ，ｋ）－临界图的一个充分必要条件。讨论了该条件的一些应用，研究了（ａ，ｂ，ｋ）－临界图的性质。     

循环图Cn〈j1,j2,…,jr,n／2〉的连通性

本文得到了奇数度循环图C_n是连通的充要条件及C_n不连通的情形.证明了三度连通循环图C_n同构于C_n<1,n/2>或C_n<2,n/2>.这一结果颇有意义.     

Hamiltonian二部竞赛图

设 T(n,n)表示 n×n 二部竞赛图。本文证明了:如果 uv 是 T(n,n)的一条弧,蕴含d~-(u) d~ (v)≥n-2≥4,则 T(n,n)是 Hamilton 图,除非 T(n,n)属于两类已被刻划的特殊图类。     

Hexavalent symmetric graphs of order 9p

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify hexavalent symmetric graphs of order $9p$ for each prime $p$.     

Hypohamiltonian Planar Cubic Graphs with Girth 5

A graph is called hypohamiltonian if it is not hamiltonian but becomes hamiltonian if any vertex is removed. Many hypohamiltonian planar cubic graphs have been found, starting with constructions of Thomassen in 1981. However, all the examples found until now had 4‐cycles. In this note we present the first examples of hypohamiltonian planar cubic graphs with cyclic connectivity 5, and thus girth 5. We show by computer search that the smallest members of this class are three graphs with 76 vertices.     

三度边正则图的三个无限族

图X称为边正则图，若X的自同构群Aut(X)在X的边集上的作用是正则的．本文考察了三度边正则图与四度Cayley图的关系，给出了一个由四度Cayley图构造三度边正则图的方法，并且构造了边正则图的三个无限族．     

Semisymmetric cubic graphs as regular covers of K 3,3

A regular graph X is called semisymmetric if it is edge-transitive but not vertex-transitive. For G ≤ AutX, we call a G-cover X semisymmetric if X is semisymmetric, and call a G-cover X one-regular if Aut X acts regularly on its arc-set. In this paper, we give the sufficient and necessary conditions for the existence of one-regular or semisymmetric Zn-Covers of K3,3. Also, an infinite family of semisymmetric Zn×Zn-covers of K3,3 are constructed.     

Edge-primitive Cayley graphs on abelian groups and dihedral groups

A graph is called edge-primitive if its automorphism group acts primitively on its edge set. In 1973, Weiss (1973) determined all edge-primitive graphs of valency three, and recently Guo et al. (2013,2015) classified edge-primitive graphs of valencies four and five. In this paper, we determine all edge-primitive Cayley graphs on abelian groups and dihedral groups.     

Classification of a family of symmetric graphs with complete 2-arc-transitive quotients

In this paper we give a classification of a family of symmetric graphs with complete 2-arc-transitive quotients. Of particular interest are two subfamilies of graphs which admit an arc-transitive action of a projective linear group. The graphs in these subfamilies can be defined in terms of the cross ratio of certain 4-tuples of elements of a finite projective line, and thus may be called the second type ‘cross ratio graphs’, which are different from the ‘cross ratio graphs’ studied in [A. Gardiner, C. E. Praeger, S. Zhou, Cross-ratio graphs, J. London Math. Soc. (2) 64 (2001), 257–272]. We also give a combinatorial characterisation of such second type cross ratio graphs.     

A Local Analysis of Imprimitive Symmetric Graphs

Let Г be a G-symmetric graph admitting a nontrivial G-invariant partition . Let Г be the quotient graph of Г with respect to . For each block B ∊ , the setwise stabiliser G_B of B in G induces natural actions on B and on the neighbourhood Г (B) of B in Г . Let G_(B) and G_[B] be respectively the kernels of these actions. In this paper we study certain “local actions" induced by G_(B) and G_[B], such as the action of G_[B] on B and the action of G_(B) on Г (B), and their influence on the structure of Г. Supported by a Discovery Project Grant (DP0558677) from the Australian Research Council and a Melbourne Early Career Researcher Grant from The University of Melbourne.     

On triconnected and cubic plane graphs on given point sets

Let S be a set of n4 points in general position in the plane, and let h<n be the number of extreme points of S. We show how to construct a 3-connected plane graph with vertex set S, having max{3n/2,n+h−1} edges, and we prove that there is no 3-connected plane graph on top of S with a smaller number of edges. In particular, this implies that S admits a 3-connected cubic plane graph if and only if n4 is even and hn/2+1. The same bounds also hold when 3-edge-connectivity is considered. We also give a partial characterization of the point sets in the plane that can be the vertex set of a cubic plane graph.     

关于一类边裂图的k-边幻性

通常没有有效的方法判别一般图G的k-边幻性.本文采用分析方法,讨论了一类非均匀边裂图SPE(Cn,h)的边幻性和k-边幻性,得到一些新的结果.