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1.
杨爱峰  林诒勋 《应用数学》2003,16(1):143-147
本文研究的问题是确定f(p,B)的值,也就是给定顶点数p和带宽B,求满足最大度不超过B的连通图的最小边数,本文给出了一些f(p,B)的值及相应极图。  相似文献   

2.
部分控制集问题是对于给定的顶点赋权图G=(V,E;c)和正整数K,寻找图G一个顶点子集T,使得在其控制下的顶点个数不小于K且T中顶点权和达到最小。本文讨论了部分控制集问题的NP-困难性;给出了该问题的一种修正Greedy近似算法,并对其近似度H(K)给出了证明。  相似文献   

3.
图的最大亏格与图的顶点划分   总被引:7,自引:0,他引:7  
黄元秋 《数学学报》2000,43(4):645-652
本文研究了图的Betti亏数与图的顶点划分的导出子图之间的关系,得到了图的最大亏格上界由其顶点划分的导出子图所表达的关系式,由此给出了图的最大亏格的一些新结果.  相似文献   

4.
讨论了由D.Stevanovi′c提出的给定顶点数n 和最大度?的非正则图的谱半径的上界,并给出了一些新的由?表示的谱半径的界.  相似文献   

5.
主要研究了图的完整度,并给出若干关于完整度的结果. 对于所有的顶点数和边数都给定的连通图类,如何确定该图类中完整度最小的图. 同时研究了对于顶点数和完整度都给定的连通图类,如何确定该图类中边数最多的图的问题. 这些结果为图的最小完整度的优化设计提供了理论和方法.  相似文献   

6.
循环图已被用于平行计算,网络等方面.循环图研究的一个基本问题是对互不同构的循环图进行计数.对于给定的一个正整数n,用C(n,k)表示互不同构的具有几个顶点,度数为k的连通循环图的个数.文中给出了度数为 4和5的循环图的一般结构,并对n=paqb(p,q皆为素数,a,b>0),给出了C(n,4)的计算公式.  相似文献   

7.
一个图的顶点子集D称为完全完备码,如果该图中的每个顶点恰与D中一个顶点相邻.给出了凯莱子集中不含2阶元的交换群上4度凯莱图的完全完备码存在的充分必要条件.  相似文献   

8.
谭尚旺  张德龙 《应用数学》2003,16(3):167-174
得到了给定顶点数和边独立数的树与单圈图的Laplacian矩阵的最大特征值的精确上界,并且给出了达到上界的所有极图.  相似文献   

9.
关于可重构的局部子图   总被引:1,自引:1,他引:0  
一个图G在一顶点x处的局部子图L{x}是由G的给定性质定义的包含x的子图L1,并以x为根,例如在点x处的k-局部子图是以x为根,以所有到x距离不超过k的顶点集合{u∈V(G):dG(v,x)≤k}为顶点集;以{uv∈E(G):dG(u,x)〈k,或dG(v,x)〈k}为边集的带根子图。本文证明了:对于G的局部子图L{x},如果每个L{x},x∈V(G),的顶点数(或边数)都小于G的顶点数(边数)减  相似文献   

10.
共轭分子的π-电子总能量可通过其相应的分子图来计算,即相应图的邻接矩阵的 特征值的绝对值之和.本文给出了具有给定匹配大小的一类树图的最小能量值和次小能 量值,并给出了达到最小能量值和次小能量值的树的刻划.  相似文献   

11.
In this paper, we present sharp bounds for the Zagreb indices, Harary index and hyper-Wiener index of graphs with a given matching number, and we also completely determine the extremal graphs.  相似文献   

12.
For a (molecular) graph, the first Zagreb index M 1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M 2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we study the Zagreb indices of n-vertex connected graphs with k cut vertices, the upper bound for M 1- and M 2-values of n-vertex connected graphs with k cut vertices are determined, respectively. The corresponding extremal graphs are characterized.  相似文献   

13.
We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have been formulated after some experiments with the programming system AutoGraphiX, designed for finding extremal graphs with respect to given properties by the use of variable neighborhood search. The conjectures are related to the maximal value of the irregularity and spectral spread in n-vertex graphs, to a Nordhaus–Gaddum type upper bound for the index, and to the maximal value of the index for graphs with given numbers of vertices and edges. None of the conjectures has been resolved so far. We present partial results and provide some indications that the conjectures are very hard.  相似文献   

14.
Frequency sequences for trees and general graphs are considered. A necessary and sufficient condition is given for a sequence of numbers to be the frequency sequence of a tree.  相似文献   

15.
The Lick-White point-partition numbers generalize the chromatic number and the point-arboricity. Similarly, uniquely (m, n)-partitionable graphs generalize uniquely m-colorable graphs.Theorem 1 gives a method for constructing uniquely (m, n)-partitionable graphs as well as a sufficient condition for a join of mn-degenerate graphs to be uniquely (m, n)-partitionable. For the case n = 1, we obtain a necessary and sufficient condition (Lemma 1). As a consequence, an embedding result for uniquely (m, 1)-partitionable graphs is obtained (Theorem 2). Finally, uniquely (m, n)-partitionable graphs with minimal connectivity are constructed (Theorem 3).  相似文献   

16.
本文研究了图的测地数.利用极点必属于测地集的方法,刻画了g(G)=n-1的图G的结构,同时使用图的一些重要参数,获得了图上下测地数的几个新的界.对于有向图D,讨论了g(D)=2的充要条件.  相似文献   

17.
In this paper, algebraic and combinatorial techniques are used to establish results concerning even signings of graphs, switching classes of signed graphs, and (?1, 1)-matrices. These results primarily deal with enumeration of isomorphism types, and determining whether there are fixed elements under the action of automorphisms. A formula is given for the number of isomorphism types of even signings of any fixed simple graph. This is shown to be equal to the number of isomorphism types of switching classes of signings of the graph. A necessary and sufficient criterion is found for all switching classes fixed by a given graph automorphism to contain signings fixed by that automorphism. It is determined whether this criterion is met for all automorphisms of various graphs, including complete graphs, which yields a known result of Mallows and Sloane. As an application, a formula is developed for the number of H-equivalence classes of (?1, 1)-matrices of fixed size. Independently, using Molien's theorem and following a suggestion of Cameron's, generating series for these numbers are given. As a final application, a necessary and sufficient condition that a square (?1, 1)-matrix be switching equivalent to a symmetric matrix is given.  相似文献   

18.
美国数学家Bondy给出了一个非负整数序列为简单图的度序列的充要条件.本文对此进行了发展,证明了一个正整数序列为连通简单图的度序列的充要条件;然后在此基础上又探讨了平面图的低度点个数问题并定义了描述连通平面图的低度点个数的一个概念φ(n,m),并对某些低阶平面图求出了φ(n,m)的值.最后给出了φ(n,m)的上下界.  相似文献   

19.
The first and second Zagreb eccentricity indices of graph G are defined as:E1(G)=∑(vi)∈V(G)εG(vi)~2,E2(G)=∑(vivj)∈E(G)εG(vi)εG(vj)whereεG(vi)denotes the eccentricity of vertex vi in G.The eccentric complexity C(ec)(G)of G is the number of different eccentricities of vertices in G.In this paper we present some results on the comparison between E1(G)/n and E2(G)/m for any connected graphs G of order n with m edges,including general graphs and the graphs with given C(ec).Moreover,a Nordhaus-Gaddum type result C(ec)(G)+C(ec)(■)is determined with extremal graphs at which the upper and lower bounds are attained respectively.  相似文献   

20.
给出了轮图W_n、扇图F_n、风车图K_2~t、图D_(m,4)、图D_(m,n)、齿轮图W_n的一般邻点可区别色指标.  相似文献   

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