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1.
应用矩阵的初等变换得到了完全五部图的 Seidel 多项式,并给出了完全五部图是S-整图的一个充分必要条件。进一步刻画了完全正则五部图和两类特殊完全五部图的Seidel谱。  相似文献   

2.
研究Laplace整图的存在性问题,通过研究完全多部图K_(a_1n_1,a_2n_2,…a_sn_s)的Laplace特征多项式,得到所有完全多部图K_(a_1n_1,a_2n_2,…a_sn_s)都是拉普拉斯整图.  相似文献   

3.
设图G是一个简单图,图G的补图记为^-G,如果G的谱都是整数,就称G是整谱图.鸡尾酒会图CP(n)=K2n-nK2(K2n是2n阶完全图)和完全图Kα都是整谱图.本文确定了图类^-αKα∪βCP(b)中的所有整谱图.  相似文献   

4.
Q整图新类     
对于一个简单图G, 方阵Q(G)=D(G)+A(G)称为G的无符号拉普拉斯矩阵,其中D(G)和A(G)分别为G的度对角矩阵和邻接矩阵. 一个图是Q整图是指该图的无符号拉普拉斯矩阵的特征值全部为整数.首先通过Stanic 得到的六个顶点数目较小的Q整图,构造出了六类具有无穷多个的非正则的Q整图. 进而,通过图的笛卡尔积运算得到了很多的Q整图类. 最后, 得到了一些正则的Q整图.  相似文献   

5.
图类aKa,a\βCP(b)中的整谱图   总被引:1,自引:0,他引:1  
设图G是一个简单图,图G的补图记为G,如果G的谱都是整数.就称G是整谱图.鸡尾酒会图CP(n)=K2n-nK2(K2n是2n阶完全图)和完全二部图K…都是整谱图.确定了图类 aKa,a∪βCP中的所有的整谱图.  相似文献   

6.
《数学理论与应用》2007,27(4):27-29
图G是一个简单,图G的补图记为^-G,如果G的谱完全由整数组成,就称G是整谱图,鸡尾酒会图CP(n)=K2n-nK2(K2n是完全图)和完全二部图Kα,α都是整谱图^[1]。^—μ1表示图类^-αKα,αUβCP(b)的一个主特征值,本文确图了当^-μ1=2b+1时,图类中^-αKα,αUβCP(b)的所有的整谱图。  相似文献   

7.
如果一个图G的选择数等于它的色数,则称该图G是色可选择的.在2002年, Ohba给出如下猜想:每一个顶点个数小于等于2X(G) 1的图G是色可选择的.容易发现Ohba猜想成立的条件是当且仅当它对完全多部图成立,但是目前只是就某些特殊的完全多部图的图类证明了Ohba猜想的正确性.在本文我们证明图K6,3,2*(k-6),1*4(k≥6)是色可选择的,从而对图K6,3,2*(k-6),1*4(k≥6)和它们的所有完全k-部子图证明了Ohba猜想成立.  相似文献   

8.
消去图、覆盖图和均匀图的若干结果   总被引:2,自引:0,他引:2  
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   

9.
用P(G,λ)表示图G的色多项式.若对任意图H,当P(H,λ)=P(G,λ)时都有H和G同构,则称图G是色唯一的.给出了以下结果:m≥2且k≥0时,完全三部图K(m,m,m+k)是色唯一的;m≥2且m+1>k≥0时,完全三部图K(m,m+1,m+k)是色唯一的.  相似文献   

10.
周兰  卜月华 《数学研究》2009,42(4):441-447
基于图G的Mycielski图M(G),研究xb(G,TG)与xb(M(G),T’)之间的关系以及xb(G,TG)与xb(M(G),T")之间的关系,其中Tc为G的生成树,T’,T"分别为M(G)的两类特殊生成树.并给出当G为二部图,完全图以及Halin图时,Xb(M(G),T")的值.  相似文献   

11.
Rosenfeld (1971) proved that the Total Colouring Conjecture holds for balanced complete r-partite graphs. Bermond (1974) determined the exact total chromatic number of every balanced complete r-partite graph. Rosenfeld's result had been generalized recently to complete r-partite graphs by Yap (1989). The main result of this paper is to prove that the total chromatic number of every complete r-partite graph G of odd order is Δ (G) + 1. This result gives a partial generalization of Bermond's theorem.  相似文献   

12.
Ore defined a graph to be geodetic if and only if there is a unique shortest path between two points, and posed the problem of characterizing such graphs. Here this problem is studied in the context of oriented graphs and such geodetic orientations are characterized first for complete graphs (geodetic tournaments), then for complete bipartite and complete tripartite graphs, and finally for complete k-partite graphs.  相似文献   

13.
设G是含有完美匹配的简单图.称图G是偶匹配可扩的(BM-可扩的),如果G的每一个导出子图是偶图的匹配M都可以扩充为一个完美匹配.极图问题是图论的核心问题之一.本文将刻画极大偶匹配不可扩图,偶图图类和完全多部图图类中的极大偶匹配可扩图.  相似文献   

14.
On bipartite zero-divisor graphs   总被引:1,自引:0,他引:1  
A (finite or infinite) complete bipartite graph together with some end vertices all adjacent to a common vertex is called a complete bipartite graph with a horn. For any bipartite graph G, we show that G is the graph of a commutative semigroup with 0 if and only if it is one of the following graphs: star graph, two-star graph, complete bipartite graph, complete bipartite graph with a horn. We also prove that a zero-divisor graph is bipartite if and only if it contains no triangles. In addition, we give all corresponding zero-divisor semigroups of a class of complete bipartite graphs with a horn and determine which complete r-partite graphs with a horn have a corresponding semigroup for r≥3.  相似文献   

15.
An edge dominating set of a graph is a set of edgesD such that every edge not inD is adjacent to an edge inD. An edge domatic partition of a graph G =(V, E) is a collection of pairwise disjoint edge dominating sets of G whose union isE. The maximum size of an edge domatic partition of G is called the edge domatic number of G. In this paper we study the edge domatic numbers of completen-partite graphs. In particular, we give exact values for the edge domatic numbers of complete 3-partite graphs and balanced complete n-partite graphs with oddn.  相似文献   

16.
A graph is S-integral (or Seidel integral) if the spectrum of its Seidel matrix consists entirely of integers. In this paper, we give a sufficient and necessary condition for complete r-partite graphs to be S-integral, from which we construct infinitely many new classes of S-integral graphs. We also present an upper bound and a lower bound for the smallest S-eigenvalue (or Seidel eigenvalue) of a complete multipartite graph.  相似文献   

17.
A graph G is m-partite if its points can be partitioned into m subsets V1,…,Vm such that every line joins a point in Vi with a point in Vj, ij. A complete m-partite graph contains every line joining Vi with Vj. A complete graph Kp has every pair of its p points adjacent. The nth interchange graph In(G) of G is a graph whose points can be identified with the Kn+1's of G such that two points are adjacent whenever the corresponding Kn+1's have a Kn in common.Interchange graphs of complete 2-partite and 3-partite graphs have been characterized, but interchange graphs of complete m-partite graphs for m > 3 do not seem to have been investigated. The main result of this paper is two characterizations of interchange graphs of complete m-partite graphs for m ≥ 2.  相似文献   

18.
We give some necessary conditions for a graph to be 3-chromatic in terms of the spectrum of the adjacency matrix. For all known distance-regular graphs it is determined whether they are 3-chromatic. A start is made with the classification of 3-chromatic distance-regular graphs, and it is shown that such graphs, if not complete 3-partite, must have λ ≤ 1.  相似文献   

19.
Polar cographs     
Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s,k)-polar if there exists a partition A,B of its vertex set such that A induces a complete s-partite graph (i.e., a collection of at most s disjoint stable sets with complete links between all sets) and B a disjoint union of at most k cliques (i.e., the complement of a complete k-partite graph).Recognizing a polar graph is known to be NP-complete. These graphs have not been extensively studied and no good characterization is known. Here we consider the class of polar graphs which are also cographs (graphs without induced path on four vertices). We provide a characterization in terms of forbidden subgraphs. Besides, we give an algorithm in time O(n) for finding a largest induced polar subgraph in cographs; this also serves as a polar cograph recognition algorithm. We examine also the monopolar cographs which are the (s,k)-polar cographs where min(s,k)?1. A characterization of these graphs by forbidden subgraphs is given. Some open questions related to polarity are discussed.  相似文献   

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