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1.
本文给出了一种构造给定直径d和围长g的测地块的方法,它是文(1)中构造法的推广,解决了文(1)中待研究的几个问题,同时对文(1)中的一错误进行了修正。  相似文献   

2.
通过剖分Petersen图我们得到了一类新的测地块.由此成功构造了给定直径为6和围长为11的测地块,解决了近二十年来悬而未决的一个存在性和构造性问题.  相似文献   

3.
构造测地块的合成法   总被引:3,自引:0,他引:3  
李德英  毛经中 《应用数学》1993,6(2):231-232
我们只讨论简单图(无环、无重边).所有未加说明的术语、记号的意义均同于[1].一个图G称为是测地的,如果它的每对点之间都被唯一的一条最短路相连接.二连通的测地图称为测地块. 关于测地块的构造方法,已有许多图论学者进行了研究.Plesnik以完全图为基础,提出了构造同胚图K_n~((i));Cook和Pryce在图类K_n~((i))的基础上进一步提出了几类图的构造;  相似文献   

4.
李相文  毛经中 《数学进展》1997,26(3):233-240
本文给出了一种新的测地块的构造方法,这种方法不同于已有的所有方法,它是由BD设计和某些已知的测地块来构造的。同时肯定地回答了Plesnik提出是否存在不同于WPd和Kn^(i)的测地块的问题。  相似文献   

5.
测地块的测地临界性   总被引:1,自引:0,他引:1  
本文证明了所有测地块都是上测地临界的,而且所有不与任何奇圈同构的测地块都是下测地临界的。因而Pathasarathy-Srinivasan猜想为真。  相似文献   

6.
测地块的测量地临界性   总被引:2,自引:0,他引:2  
本文证明了所有测地块都是上测地临界的,而且所有不与任何奇圈构的测地块都是下地临界的。因而Pathasarathy-Srinivasan猜想为真。  相似文献   

7.
主要讨论了群环Z_nG的基于理想△(G)的零因子图Γ_(△(G))(Z_nG)的性质,分别给出了Γ_(△(G))(Z_nG)的围长,平面性和直径的详细刻画.同时,给出了交换环R基于其理想I的零因子图Γ_I(R)与商环R/I的零因子图Γ(R/I)的直径的关系的一个刻画.  相似文献   

8.
从河流的弯曲现象出发,分别在平面直角坐标系与极坐标系下构造了一类弧段上任一点到起点的弧长与弦长成π倍的理想曲线,探讨了该类曲线的存在性与唯一性.最后,将所得结论推广至空间中弧长与弦长成k倍的情形.  相似文献   

9.
研究了与频道分配有关的一种染色-(p,1)-全标号.通过在一个顶点粘结不同的简单图构造了几类有趣图,根据所构造图的特征,利用穷染法,给出了一种标号方法,得到了平凡和非平凡叶子图Gm,4、风车图K3t和图Dm,n的(2,1)-全标号数.(p,1)-全标号是对图的全染色的一种推广.  相似文献   

10.
黄保军 《大学数学》2008,24(3):136-139
具体刻画了柱面、锥面、旋转曲面上测地线的几何特征,所得结果一方面匡正了某些文献关于锥面上测地线的错误断言,一方面推广了现有文献关于旋转曲面上测地线几何性质的描述.  相似文献   

11.
A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of GX must have at least two vertices. The restricted connectivity κ(G) of a connected graph G is defined as the minimum cardinality of a restricted cut. Additionally, if the deletion of a minimum restricted cut isolates one edge, then the graph is said to be super-restricted connected. In this paper, several sufficient conditions yielding super-restricted-connected graphs are given in terms of the girth and the diameter. The corresponding problem for super-edge-restricted-connected graph is also studied.  相似文献   

12.
Ostrand posed the following two questions in 1973. (1) What is the maximum girth of a graph with radius r and diameter d? (2) What is the minimum circumference of a graph with radius r and diameter d? Question 2 has been answered by Hrn?iar who proves that if d2r?2 the minimum circumference is 4r?2d. In this note we first answer Question 1 by proving that the maximum girth is 2r+1. This improves on the obvious upper bound 2d+1 and implies that every Moore graph is self-centered. We then prove a property of the blocks of a graph which implies Hrn?iar’s result.  相似文献   

13.
变换图的直径及Brualdi猜想   总被引:1,自引:0,他引:1  
钱建国 《数学学报》2002,45(2):411-416
设R=(r1,r2…rm)及 S=(S1,S2,…,Sn)为两个正整数向量,满足Σmi=1ri=Σnj=1sj= K.记G(R,S)为(0,1)-矩阵类 U(R,S)的变换图.Brualdi在文山中给出了 G(R,S)的直径厂(G(R,S))的一个上界:mn/2-1,并猜想D(G(R,S))≤mn/4.本文通过对有向图围长的研究得到了D(G(R,S))的一个新的上界:1/2mn-1/6t(t-1)(4t+1),其中T=  .  相似文献   

14.
In this paper, first we prove that any graph G is 2-connected if diam(G)≤g−1 for even girth g, and for odd girth g and maximum degree Δ≤2δ−1 where δ is the minimum degree. Moreover, we prove that any graph G of diameter diam(G)≤g−2 satisfies that (i) G is 5-connected for even girth g and Δ≤2δ−5, and (ii) G is super-κ for odd girth g and Δ≤3δ/2−1.  相似文献   

15.
16.
The restricted connectivity κ(G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex u has all its neighbors in X; the superconnectivity κ1(G) is defined similarly, this time considering only vertices u in G-X, hence κ1(G)?κ(G). The minimum edge-degree of G is ξ(G)=min{d(u)+d(v)-2:uvE(G)}, d(u) standing for the degree of a vertex u. In this paper, several sufficient conditions yielding κ1(G)?ξ(G) are given, improving a previous related result by Fiol et al. [Short paths and connectivity in graphs and digraphs, Ars Combin. 29B (1990) 17-31] and guaranteeing κ1(G)=κ(G)=ξ(G) under some additional constraints.  相似文献   

17.
Short, elementary proofs of the optimal bounds for various path and cycle lengths are given for the zero-divisor graphs and digraphs of semigroups.  相似文献   

18.
A graph is superconnected, for short super-κ, if all minimum vertex-cuts consist of the vertices adjacent with one vertex. In this paper we prove for any r-regular graph of diameter D and odd girth g that if Dg−2, then the graph is super-κ when g≥5 and a complete graph otherwise.  相似文献   

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