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 共查询到18条相似文献,搜索用时 78 毫秒
1.
In this paper,we study the bases and base sets of primitive symmetric loop-free (generalized)signed digraphs on n vertices.We obtain sharp upper bounds of the bases,and show that the base sets of the classes of such digraphs are{2,3,...,2n-1}.We also give a new proof of an important result obtained by Cheng and Liu.  相似文献   

2.
Let S be a primitive non-powerful symmetric loop-free signed digraph on even n vertices with base 3 and minimum number of arcs. In [Lihua YOU, Yuhan WU. Primitive non-powerful symmetric loop-free signed digraphs with given base and minimum number of arcs. Linear Algebra Appl., 2011, 434(5), 1215-1227], authors conjectured that D is the underlying digraph of S with exp(D) = 3 if and only if D is isomorphic to ED n,3,3 , where ED n,3,3 = (V, A) is a digraph with V = {1, 2, . . . , n}, A = {(1, i), (i, 1) | 3≤i≤n} ∪ {(2i-1, 2i), (2i, 2i-1) | 2≤i≤ n/2 } ∪ {(2, 3), (3, 2), (2, 4), (4, 2)}). In this paper, we show the conjecture is true and completely characterize the underlying digraphs which have base 3 and the minimum number of arcs.  相似文献   

3.
Denote by c,(s)the circulant digraph with vertex set zn=[0,1,2……n-1]and symbol set s(≠-s)∈zn\[0].let x be the automorphism group of cn(S)and xo the stabilizer of o in x.then cn(S)is arctransitive if and only if xo acts transitively on s.in this paper,co(S)with xo is being the symmetric group is characterized by its symbot set .by the way all the arctransitive clcculant digraphs of degree 2are given.  相似文献   

4.
LARGEST EIGENVALUE OF A UNICYCLIC MIXED GRAPH   总被引:3,自引:0,他引:3  
The graphs which maximize and minimize respectively the largest eigenvalue over all unicyclic mixed graphs U on n vertices are determined. The unicyclic mixed graphs U with the largest eigenvalue λ1 (U)=n or λ1 (U)∈ (n ,n 1] are characterized.  相似文献   

5.
陈佘喜  胡亚辉 《东北数学》2004,20(4):424-434
This paper first establishes a distance inequality of the associated diagraph of a central symmetric primitive matrix, then characters the exponent set of central symmetric primitive matrices, and proves that the exponent set of central symmetric primitive matrices of order n is {1, 2,… ,n-1}. There is no gap in it.  相似文献   

6.
BOUNDS OF EIGENVALUES OF A GRAPH   总被引:3,自引:0,他引:3  
Let G be a simple graph with n vertices.We denote by λ_i(G) the i-th largest eigenvalue of G.In this paper,several results are presented concerning bounds on the eigenvalues of G.In particular,it is shown that -1≤λ_2(G)≤(n-2)/2,and the left hand equality holds if and only if G is a complete graph with at least two vertices;the right hand equality holds if and only if n is even and G?2K_(n/2).  相似文献   

7.
Let Γ be a signed graph and A(Γ) be the adjacency matrix of Γ. The nullity ofΓ is the multiplicity of eigenvalue zero in the spectrum of A(Γ). In this paper, the connected bicyclic signed graphs(including simple bicyclic graphs) of order n with nullity n-7 are completely characterized.  相似文献   

8.
Restricted Fault Diameter of Hypercube Networks   总被引:1,自引:0,他引:1  
This paper studies restricted fault diameter of the n-dimensional hypercube networks Qn (n ≥ 2).It is shown that for arbitrary two vertices x and y with the distance d in Qn and any set F with at most 2n-3 vertices in Qn - {x, y}, if F contains neither of neighbor-sets of x and y in Qn, then the distance between x andy in Qn - F is given by D(Qn-F;x,y){=1 , for=1;≤d 4 , for 2≤d≤n-2,n≥4;≤n 1, for d=n-1,n≥3; =n, for d=n. Furthermore, the upper bounds are tight. As an immediately consequence, Qn can tolerate up to 2n-3 vertices failures and remain diameter 4 if n = 3 and n 2 if n ≥ 4 provided that for each vertex x in Qn, all the neighbors of x do not fail at the same time. This improves Esfahanian‘s result.  相似文献   

9.
Let G be a simple graph with 2n vertices and a perfect matching.The forcing number f(G,M) of a perfect matching M of G is the smallest cardinality of a subset of M that is contained in no other perfect matching of G.Among all perfect matchings M of G,the minimum and maximum values of f(G,M) are called the minimum and maximum forcing numbers of G,denoted by f(G) and F(G),respectively.Then f(G)≤F(G) ≤n-1.Che and Chen(2011) proposed an open problem:how to characterize the graphs G with f(G)=n-1.Lat...  相似文献   

10.
Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs,and it has become an active research issue in recent years.Tang et al.derived upper and lower bounds on the maximum number of clear two-factor interactions(2fi's) in 2n-(n-k) fractional factorial designs of resolutions III and IV by constructing a 2n-(n-k) design for given k,which are only restricted for the symmetrical case.This paper proposes and studies the clear effects problem for the asymmetrical case.It improves the construction method of Tang et al.for 2n-(n-k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components(2fic's) in 4m2n designs with resolutions III and IV.The lower bounds are achieved by constructing specific designs.Comparisons show that the number of clear 2fic's in the resulting design attains its maximum number in many cases,which reveals that the construction methods are satisfactory when they are used to construct 4m2n designs under the clear effects criterion.  相似文献   

11.
In this article, we study the kth upper and lower bases of primitive nonpowerful minimally strong signed digraphs. A bound on the kth upper bases for primitive nonpowerful minimally strong signed digraphs is obtained, and the equality case of the bound is characterized. For the kth lower bases, we obtain some bounds. For some cases, the bounds are best possible and the extremal signed digraphs are characterized. We also show that there exist ‘gaps’ in both the kth upper base set and the kth lower base set of primitive nonpowerful minimally strong signed digraphs.  相似文献   

12.
一个本原不可幂带号有向图s的基指数l(s)是这样的最小正整数l,使得在s中,从任意一点u到任意一点v都有一对长为l的sssD途径.本文研究了n阶最小奇圈长为r的本原不可幂对称带号有向图的基指数,给出了这类有向图的基指数的最大值.  相似文献   

13.
The atom-bond connectivity(ABC) index of a graph G, introduced by Estrada,Torres, Rodr′?guez and Gutman in 1998, is defined as the sum of the weights(1/di+1/dj-2/didj )~(1/2) of all edges vivj of G, where di denotes the degree of the vertex vi in G. In this paper, we give an upper bound of the ABC index of a two-tree G with n vertices, that is, ABC(G) ≤(2n- 4)2~(1/2)/2+(2n-4)~(1/2)/n-1. We also determine the two-trees with the maximum and the second maximum ABC index.  相似文献   

14.
In [B.M. Kim, B.C. Song, W. Hwang, Primitive graphs with given exponents and minimum number of edges, Linear Algebra Appl. 420 (2007) 648-662], the minimum number of edges of a simple graph on n vertices with exponent k was determined. In this paper, we completely determine the minimum number, H(n,k), of arcs of primitive non-powerful symmetric loop-free signed digraphs on n vertices with base k, characterize the underlying digraphs which have H(n,k) arcs when k is 2, nearly characterize the case when k is 3 and propose an open problem.  相似文献   

15.
In [J. Shao, L. You, H. Shan, Bound on the bases of irreducible generalized sign pattern matrices, Linear Algebra Appl. 427 (2007) 285-300], the authors extended the concept of the base from powerful sign pattern matrices to non-powerful irreducible sign pattern matrices. Recently, the kth local bases and the kth upper bases, which are generalizations of the bases, of primitive non-powerful signed digraphs were introduced. In this paper, we introduce a new parameter called the kth lower bases of primitive non-powerful signed digraphs and obtain some bounds for it. For some cases, the bounds we obtain are best possible and the extremal signed digraphs are characterized, respectively. Moreover, we show that there exist “gaps” in the kth lower bases set of primitive non-powerful signed digraphs.  相似文献   

16.
设n≥5,D为n阶强连通竞赛图,本文给出了本原指数达到次大值n 1的极图的完全刻画.  相似文献   

17.
两个围长为2的本原不可幂定号有向图的广义基   总被引:1,自引:0,他引:1  
研究了两个围长为2的本原定号有向图,通过对图形的分析,综合运用本原指数,SSSD途径对,Frobenius指数的结论和特性,推导出了这两个图形的广义基.  相似文献   

18.
一个三色有向图D是本原的,当且仅当存在非负整数h、k和v,且h+k+v0,使得D中的每一对顶点(i,j)都存在从i到j的(h,k,v)-途径,h+k+v的最小值定义为三色有向图D的本原指数.研究了一类三色有向图,它的未着色图中包含2佗-4个顶点,一个n-圈、一个(n-2)-圈和一个2-圈,给出了本原指数上界.  相似文献   

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