The non-solvability by radicals of generic 3-connected planar Laman graphs

We show that planar embeddable -connected Laman graphs are generically non-soluble. A Laman graph represents a configuration of points on the Euclidean plane with just enough distance specifications between them to ensure rigidity. Formally, a Laman graph is a maximally independent graph, that is, one that satisfies the vertex-edge count together with a corresponding inequality for each subgraph. The following main theorem of the paper resolves a conjecture of Owen (1991) in the planar case. Let be a maximally independent -connected planar graph, with more than 3 vertices, together with a realisable assignment of generic distances for the edges which includes a normalised unit length (base) edge. Then, for any solution configuration for these distances on a plane, with the base edge vertices placed at rational points, not all coordinates of the vertices lie in a radical extension of the distance field.

     

Score sets in oriented 3-partite graphs

Let D(U, V, W) be an oriented 3-partite graph with |U|=p, |V|=q and |W|= r. For any vertex x in D(U, V, W), let d x and d-x be the outdegree and indegree of x respectively. Define aui (or simply ai) = q r d ui - d-ui, bvj(or simply bj) = p r d vj - d-vj and Cwk (or simply ck) = p q d wk - d-wk as the scores of ui in U, vj in V and wk in Wrespectively. The set A of distinct scores of the vertices of D(U, V, W) is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai(2≤i≤n - 1) are even positive integers and an is any positive integer, then for n≥3, there exists an oriented 3-partite graph with the score set A = {a1,2∑i=1 ai,…,n∑i=1 ai}, except when A = {0,2,3}. Some more results for score sets in oriented 3-partite graphs are obtained.     

关于—类(p_1,p_2)—图的自同构群

在本文中,作者利用陪集图成功地推广了D.Goldshmidt在[1]中的工作。     

Using Fractal Function Auto correlative Method to Confirm Fractal Dimension of Function Graph

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｈｙｐｏｔｈｅｓｉｓｏｆａｓｔａｔｉｓｔｉｃａｌｙｌｏｃａｌｙｉｓｏｔｒｏｐｉｃｈｏｍｏｇｅｎｅｏｕｓｔｕｒｂｕｌｅｎｔｆｉｅｌｄｗａｓｔｈｅｂａｓｅｏｆＫｏｌｍｏｇｏｒｏｖ’ｓｍｏｄｅｌ［１］．Ｔｈｅｓｅｃｏｎｄｏ...     

A POLYNOMIAL ALGORITHM FOR FINDING THE MINIMUM FEEDBACK VERTEX SET OF A 3-REGULAR SIMPLE GRAPH

1IntroductionLetG=(VE)beaconnectedsimplegraph.AsubsetFofvertexsetViscalIedafeedbackvertexsetofGifthegraPhGFisaf0rest.ThecardinaIity0faminimumfeedbackvertexset0fGisdenotedbyf(G).AvertexsubsetJofvertexsetViscaJledallonseparatingindependentsetofG,ifJisanilldependentsetofVandGJisconnected.Thema-xiammcardinalityofnollseparatingindependelltsetofGisden0tedbyz(G)andiscalledthenonseparatingindepelldentnumberofG,AgraphGiscalledacactusifGisc0nnectedandanytwocyclesofGaredisjoint.Avertexvofacon…     

Graphs with Branchwidth at Most Three

In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph as a minor. A set of four graphs is shown to be the obstruction set for the class of graphs with branchwidth at most three. Moreover, we give a safe and complete set of reduction rules for the graphs with branchwidth at most three. Using this set, a linear time algorithm is given that verifies if a given graph has branchwidth at most three, and, if so, outputs a minimum width branch decomposition.     

最小次数至少为4的超欧拉图

设Ｇ是２－边－连通的ｎ阶图。假设对任何的的最小边割集Ｅ等于包含于Ｅ（Ｇ）且│Ｅ│≤３,Ｇ－Ｅ的每个分支的阶至少为ｎ／５,则或者Ｇ是一个超欧拉图或者Ｇ有５个互不相交的阶数为ｎ／５连通分支,当这５个分支都收缩时,Ｇ收缩为Ｋ２,３,这个结果推广了蔡小涛,Ｐ．Ａ．Ｃａｔｌｉｎ,Ｆ．Ｊａｅｇｅｒ和Ｈ．Ｊ．Ｌａｉ等人关于超欧拉图的结果。     

筛选式群体评价模型及算法

本文提供一种带筛选功能的群体评价数学模型和相应算法,使评价结果能充分体现评价者的参评水平。     

交通网络连通性表达法的研究

通过对增设虚拟边网络连通性表达法和对偶图网络连通性表达法的描述和它们所面临问题的分析研究,说明这两种方法在交通网络连通性表达上,尤其是在引进交通转弯限制时所显示出来的需要大量处理工作的问题,提出了一种新的网络连通性表达法,作者称为“边标号法”,此法避免了对交通网络增设虚拟边或进行点边转化所带来的大量工作量问题,在对交通网络图不作任何修改的情况下,清楚而有效地表达出网络的连通特性。并用一个具体实例通过程序实现该方法,体现出了边标号法的优越性     

最短时限运输问题及图上求解法

提出了最短时限运输问题,借助于赋权二分图研究了其解的最优性充要条件,并给出了在赋权二分图上求解的具体步骤,最后给出了一个实例。事实证明,该法是一个有效的算法