首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 93 毫秒
1.
For a digraph D, let L(D) and S(D) denote its line digraph and subdivision digraph, respectively. The motivation of this paper is to solve the digraph equation L(S(D))=S(L(D)). We show that L(S(D)) and S(L(D)) are cospectral if and only if D and L(D) have the same number of arcs. Further, we characterize the situation that L(S(D)) and S(L(D)) are isomorphic. Our approach introduces the new notion, the proper image D* of a digraph D, and a new type of connectedness for digraphs. The concept D* plays an important role in the main result of this paper. It is also useful in other aspects of the study of line digraphs. For example, L(D) is connected if and only if D* is connected; L(D) is functional (contrafunctional) if and only if D* is functional (contrafunctional). Some related results are also presented.  相似文献   

2.
We characterize the equality case of the upper bound γ(D) ? n + s(n ? 2) for the exponent of a primitive digraph in the case s ? 2, where n is the number of the vertices of the digraph D and s is the length of the shortest elementary circuit of D. We also answer a question about the equality case when s = 1. The exponent of an n × n primitive nonnegative matrix A is the same as the exponent of the associated digraph D(A) of A. So every theorem in this paper can be translated into a theorem about nonnegative matrices.  相似文献   

3.
A digraph D is oriented if it does not contain 2-cycles.If an oriented digraph D has a directed eulerian path,it is an oriented eulerian digraph.In this paper,when an oriented eulerian digraph D has minimum out-degree 2 and a diameter d,we find the minimum order of D.In addition,when D is 2-regular with diameter 4m(m ≥ 2),we classify the extremal cases.  相似文献   

4.
In this paper we determine the positive integers n and k for which there exists a homogeneous factorisation of a complete digraph on n vertices with k ‘common circulant’ factors. This means a partition of the arc set of the complete digraph Kn into k circulant factor digraphs, such that a cyclic group of order n acts regularly on the vertices of each factor digraph whilst preserving the edges, and in addition, an overgroup of this permutes the factor digraphs transitively amongst themselves. This determination generalises a previous result for self-complementary circulants.  相似文献   

5.
Let D be a digraph. By γ(D) we denote the domintaion number of D and by D we denote a digraph obtained by reversing all the arcs of D. In this paper we prove that for every δ≥3 and k≥1 there exists a simple strongly connected δ-regular digraph Dδ,k such that . Analogous theorem is obtained for total domination number provided that δ≥4.  相似文献   

6.
Let S(1),…,S(n),T(1),…,T(n) be random subsets of the set [m]={1,…,m}. We consider the random digraph D on the vertex set [n] defined as follows: the arc ij is present in D whenever S(i)∩T(j)≠0?. Assuming that the pairs of sets (S(i),T(i)), 1≤in, are independent and identically distributed, we study the in- and outdegree distributions of a typical vertex of D as n,m.  相似文献   

7.
A digraph D is connected if the underlying undirected graph of D is connected. A subgraph H of an acyclic digraph D is convex if there is no directed path between vertices of H which contains an arc not in H. We find the minimum and maximum possible number of connected convex subgraphs in a connected acyclic digraph of order n. Connected convex subgraphs of connected acyclic digraphs are of interest in the area of modern embedded processors technology.  相似文献   

8.
In this paper we give a criterion for the adjacency matrix of a Cayley digraph to be normal in terms of the Cayley subset S. It is shown with the use of this result that the adjacency matrix of every Cayley digraph on a finite group G is normal iff G is either abelian or has the form for some non-negative integer n, where Q8 is the quaternion group and is the abelian group of order 2n and exponent 2.  相似文献   

9.
10.
By definition, a vertex w of a strongly connected (or, simply, strong) digraph D is noncritical if the subgraph D — w is also strongly connected. We prove that if the minimal out (or in) degree k of D is at least 2, then there are at least k noncritical vertices in D. In contrast to the case of undirected graphs, this bound cannot be sharpened, for a given k, even for digraphs of large order. Moreover, we show that if the valency of any vertex of a strong digraph of order n is at least 3/4n, then it contains at least two noncritical vertices. The proof makes use of the results of the theory of maximal proper strong subgraphs established by Mader and developed by the present author. We also construct a counterpart of this theory for biconnected (undirected) graphs.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号