共查询到20条相似文献,搜索用时 125 毫秒
1.
2.
设T为n阶强连通竞赛图.本文通过详细刻画不能进行圈分解的强连通竞赛图的特征,证明了满足max{^ ,δ^-}≥5k-5和k≥2的强连通竞赛图T,能够分解为k个圈. 相似文献
3.
林育青 《纯粹数学与应用数学》2017,33(1)
该文定义了图(C)2n,并研究了该图的奇优美和奇强协调性.利用构造法分别给出了图(C)2n在n=4k(k≥2)、n=4k+2时的奇优美算法,在n=4kk≥2)时,的奇强协调算法,进而证明了图(C)2n在n=2k(k≥3)时是奇优美图,在n=4k(k≥2)时是奇强协调图等结论,从而推动了对图的奇优美性和奇强协调性的研究.最后提出猜想:当n=4k+2时,图(C)2n不是奇强协调图. 相似文献
4.
轮图的广义Mycielski图的邻强边色数 总被引:3,自引:0,他引:3
设图 G(V,E)为简单图 ,V(Mn(G) ) |{ v0 1,v0 2 ,… ,v0 p;v11,v12 ,… ,v1p,… ,vn1,vn2 ,… ,vnp}E(Mn(G) ) =E(G)∪ { vijv(i+ 1) k|v0 jv0 k ∈ E(G) ,1≤ j,k≤ p ,i =0 ,1,… ,n - 1}称 Mn(G)为 G的 n广义 Mycielski图 ,n为自然数 .本文得到了轮的广义 Mycielski图的临强边色数 . 相似文献
5.
6.
7.
m-K_n-残差图是由P.Erds,F.Harary和M.Klawe等人提出的,当m=1时,他们证明了当n≠1,2,3,4时,K_(n+1)×K_2是唯一的具有最小阶的连通的K_n-残差图.首先得到了m-K_n-残差图的重要性质,同时证明了当n=1,2,3,4时,连通K_n-残差图的最小阶和极图,其中当n=1,2时得到唯一极图;当n=3,4时,证明了恰有两个不同构的极图,从而彻底解决连通的K_n-残差图的最小阶和极图问题.最后证明了当n≠1,2,3,4时,K_(n+1)×K_2是唯一的具有最小阶的连通的K_n-残差图. 相似文献
8.
对强连通有向图D的一个非空顶点子集S,D中包含S的具有最少弧数的强连通有向子图称为S的Steiner子图,S的强Steiner距离d(S)等于S的Steiner子图的弧数. 如果|S|=k, 那么d(S)称为S的k-强距离. 对整数k≥2和强有向图D的顶点v,v的k-强离心率sek(v)为D中所有包含v的k个顶点的子集的k-强距离的最大值. D中顶点的最小k-强离心率称为D的k-强半径,记为sradk(D),最大k-强离心率称为D的k-强直径,记为sdiamk(D). 本文证明了,对于满足k+1≤r,d≤n的任意整数r,d,存在顶点数为n的强竞赛图T′和T″,使得sradk(T′)=r和sdiamk(T″)=d;进而给出了强定向图的k-强直径的一个上界. 相似文献
9.
10.
11.
12.
关于图P_n~3优美性的研究 总被引:1,自引:0,他引:1
在n个顶点的路Pn上,当且仅当两点的距离为3时增加一条边,所得的图称为P3n,本文给出了图P3n(n≥4)的优美标号,从而证明了P3n都是优美图. 相似文献
13.
林跃峰 《数学的实践与认识》2013,43(10)
研究次极大图(即链环分支数等于基圈数的连通平图)的唯一性.证明了无割点且包含子图K_4的连通平图G是次极大图当且仅当G同构于K_4,并刻画了包含子图K_4的次极大图的结构. 相似文献
14.
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
15.
对于简单图G=〈V,E〉,如果存在一个映射f:V(G)→{0,1,2,…,2|E|-1}满足:1)对任意的u,v∈V,若u≠v,则f(u)≠f(v);2)max{f(v)|v∈V}=2|E|-1;3)对任意的e_1,e_2∈E,若e_1≠e_2,则g(e_1)≠g(e_2),此处g(e)=|f(u)+f(v)|,e=uv;4)|g(e)|e∈E}={1,3,5,…,2|E|-1},则称G为奇优美图,f称为G的奇优美标号.设G=〈V,E〉是一个无向简单图.如果存在一个映射f:V(G)→{0,1,2,…,2|E|-1},满足:1)f是单射;2)■uv∈E(G),令f(uv)=f(u)+f(v),有{f(uv)|uv∈E(G)}={1,3,5,…,2|E|-1},则称G是奇强协调图,f称为G的.奇强协调标号或奇强协调值.给出了链图、升降梯等几类有趣图的奇优美标号和奇强协调标号. 相似文献
16.
17.
Strongly Regular Decompositions of the Complete Graph 总被引:3,自引:0,他引:3
Edwin R. van Dam 《Journal of Algebraic Combinatorics》2003,17(2):181-201
We study several questions about amorphic association schemes and other strongly regular decompositions of the complete graph. We investigate how two commuting edge-disjoint strongly regular graphs interact. We show that any decomposition of the complete graph into three strongly regular graphs must be an amorphic association scheme. Likewise we show that any decomposition of the complete graph into strongly regular graphs of (negative) Latin square type is an amorphic association scheme. We study strongly regular decompositions of the complete graph consisting of four graphs, and find a primitive counterexample to A.V. Ivanov's conjecture which states that any association scheme consisting of strongly regular graphs only must be amorphic. 相似文献
18.
We obtain a convenient expression for the parameters of a strongly regular graph with k=2 in terms of the nonprincipal eigenvalues x and –y. It turns out in particular that such graphs are pseudogeometric for pG
x(2x,y–1). We prove that a strongly regular graph with parameters (35,16,6,8) is a quotient of the Johnson graph
(8,4). We also find the parameters of strongly regular graphs in which the neighborhoods of vertices are pseudogeometric graphs for pG
x(2x,t),x3. In consequence, we establish that a connected graph in which the neighborhoods of vertices are pseudogeometric graphs for pG
3(6,2) is isomorphic to the Taylor graph on 72 vertices or to the alternating form graph Alt(4,2) with parameters (64,35,18,20). 相似文献
19.
设 H(K_{1,5},P_n,C_l)是由路 P_n的两个悬挂点分别粘上星图K_{1,5}的悬挂点和圈 C_l的点所得的单圈图. 若两个二部图是关于Laplacian 矩阵同谱的, 则它们的线图是邻接同谱的, 两个邻接同谱图含有相同数目的同长闭回路. 如果任何一个与图G关于Laplacian 同谱图都与图G 同构, 那么称图G可由其Laplacian 谱确定. 利用图与线图之间的关系证明了H(K_{1,5},P_n,C_4)、H(K_{1,5},P_n,C_6) 由它们的Laplacian谱确定. 相似文献
20.
For every simple graph G,a class of multiple clique cluster-whiskered graphs Geπm is introduced,and it is shown that all such graphs are vertex decomposable;thus,the independence simplicial complex IndGeπm is sequentially Cohen-Macaulay.The properties of the graphs Geπm and Gπ constructed by Cook and Nagel are studied,including the enumeration of facets of the complex Ind Gπ and the calculation of Betti numbers of the cover ideal Ic(Geπ").We also prove that the complex △ =IndH is strongly shellable and pure for either a Boolean graph H =Bn or the full clique-whiskered graph H =Gw of G,which is obtained by adding a whisker to each vertex of G.This implies that both the facet ideal I(△) and the cover ideal Ic(H) have linear quotients. 相似文献