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1.
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
2.
For a strongly connected digraph D the minimum ,cardinality of an arc-cut over all arc-cuts restricted arc-connectivity λ′(D) is defined as the S satisfying that D - S has a non-trivial strong component D1 such that D - V(D1) contains an arc. Let S be a subset of vertices of D. We denote by w+(S) the set of arcs uv with u ∈ S and v S, and by w-(S) the set of arcs uv with u S and v ∈ S. A digraph D = (V, A) is said to be λ′-optimal if λ′(D) =ξ′(D), where ξ′(D) is the minimum arc-degree of D defined as ξ(D) = min {ξ′(xy) : xy ∈ A}, and ξ′(xy) = min(|ω+({x,y})|, |w-({x,y})|, |w+(x) ∪ w- (y) |, |w- (x) ∪ω+ (y)|}. In this paper a sufficient condition for a s-geodetic strongly connected digraph D to be λ′-optimal is given in terms of its diameter. Furthermore we see that the h-iterated line digraph Lh(D) of a s-geodetic digraph is λ′-optimal for certain iteration h. 相似文献
3.
Let D be a digraph.The competition graph of D is the graph having the same vertex set with D and having an edge joining two different vertices if and only if they have at least one common out-neighbor in D.The phylogeny graph of D is the competition graph of the digraph constructed from D by adding loops at all vertices.The competition/phylogeny number of a graph is the least number of vertices to be added to make the graph a competition/phylogeny graph of an acyclic digraph.In this paper,we show that for any integer k there is a connected graph such that its phylogeny number minus its competition number is greater than k.We get similar results for hypergraphs. 相似文献
4.
A linear directed forest is a directed graph in which every component is a directed path.The linear arboricity la(D) of a digraph D is the minimum number of linear directed forests in D whose union covers all arcs of D. For every d-regular digraph D, Nakayama and P′eroche conjecture that la(D) = d + 1. In this paper, we consider the linear arboricity for complete symmetric digraphs,regular digraphs with high directed girth and random regular digraphs and we improve some wellknown results. Moreover, we propose a more precise conjecture about the linear arboricity for regular digraphs. 相似文献
5.
巫世权 《数学物理学报(B辑英文版)》1988,(1)
The topic, posets and graphs, recently comes about as a new branch of combinatorics. This paper is one on the topic.Trying to solve a research problem posed by Trotter in [1]. we constructively prove the following theorem of the necessary and sufficient conditions for a digraph to be a posetable digraph.Theorem. A digraph D is a posetable digraph if and only if D—a contains no directed path between u and v for any arc a=(u, v) of D. 相似文献
6.
In this paper, we define a class of strongly connected digraph, called the k-walk- regular digraph, study some properties of it, provide its some algebraic characterization and point out that the 0-walk-regular digraph is the same as the walk-regular digraph discussed by Liu and Lin in 2010 and the D-walk-regular digraph is identical with the weakly distance-regular digraph defined by Comellas et al in 2004. 相似文献
7.
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
8.
Jiong-sheng Li Kai Yang Qing-xue WangDepartment of Mathematics University of Science Technology of China Hefei China 《应用数学学报(英文版)》2002,18(3):471-476
A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs. 相似文献
9.
A digraph D is supereulerian if D has a spanning eulerian subdigraph. BangJensen and Thomass′e conjectured that if the arc-strong connectivity λ(D) of a digraph D is not less than the independence number α(D), then D is supereulerian. In this paper, we prove that if D is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfyingλ(D) ≥α(D), then D is supereulerian. 相似文献
10.
Hongxia Ma & Juan Liu 《数学研究通讯:英文版》2016,32(4):332-338
Let γ*(D) denote the twin domination number of digraph D and let D_1 D_2 denote the strong product of D_1 and D_2. In this paper, we obtain that the twin domination number of strong product of two directed cycles of length at least 2.Furthermore, we give a lower bound of the twin domination number of strong product of two digraphs, and prove that the twin domination number of strong product of the complete digraph and any digraph D equals the twin domination number of D. 相似文献
11.
In this paper, we generalize the concept of asymptotic Hankel operators on H2(D) to the Hardy space H2(Dn) (over polydisk) in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence. Meanwhile, we introduce ith-partial Hankel operators on H2(Dn) and obtain a characterization of its compactness for n > 1. Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H2(Dn). It is also shown that a Toeplitz operator with symbol φ is asymptotic Hankel if and only if φ is holomorphic function in L∞(Tn). 相似文献
12.
Namita Das 《印度理论与应用数学杂志》2010,41(2):379-400
In this paper the concept of asymptotic Toeplitz and asymptotic Hankel operators on the Bergman space are introduced and properties of these classes of operators are studied. The importance of this notion is that it associates with a class of operators a Toeplitz operator and with a class of operators a Hankel operator where the original operators are not even Toeplitz or Hankel. Thus it is possible to assign a symbol to an operator that is not Toeplitz or Hankel and hence a symbol calculus is obtained. Further a relation between Toeplitz operators and little Hankel operators on the Bergman space is established in some asymptotic sense. 相似文献
13.
本文研究了单位圆盘D 的Dirichlet 空间上Toeplitz 算子和小Hankel 算子. 利用Berezin 型变换讨论了Toeplitz 算子的不变子空间问题, 具有Berezin 型符号的Toeplitz 算子的渐进可乘性以及Toeplitz 算子的Riccati 方程的可解性. 应用Berezin 变换得到了Toeplitz 算子和小Hankel 算子可逆的充分条件. 此外, 还利用Hankel 算子和Berezin 变换刻画了算子2Tuv-TuTv-TvTu 的紧性, 其中函数u,v ∈ L2,1. 相似文献
14.
In this paper we consider a class of weighted integral operators onL
2 (0, ) and show that they are unitarily equivalent to Hankel operators on weighted Bergman spaces of the right half plane. We discuss conditions for the Hankel integral operator to be finite rank, Hilbert-Schmidt, nuclear and compact, expressed in terms of the kernel of the integral operator. For a particular class of weights these operators are shown to be unitarily equivalent to little Hankel operators on weighted Bergman spaces of the disc, and the symbol correspondence is given. Finally the special case of the unweighted Bergman space is considered and for this case, motivated by approximation problems in systems theory, some asymptotic results on the singular values of Hankel integral operators are provided. 相似文献
15.
We establish an asymptotic formula for determinants of truncated
Wiener-Hopf+Hankel operators with symbol equal to the exponential of a constant
times the characteristic function of an interval. This is done by reducing
it to the corresponding (known) asymptotics for truncated Toeplitz+Hankel
operators. The determinants in question arise in random matrix theory in determining
the limiting distribution for the number of eigenvalues in an interval
for a scaled Laguerre ensemble of positive Hermitian matrices. 相似文献
16.
Sungeun Jung 《中国科学 数学(英文版)》2018,(5)
Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S~(*n)T S~n}is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H.In this paper,we study the asymptotic T_u-Toeplitzness of weighted composition operators on the Hardy space H~2,where u is a nonconstant inner function. 相似文献
17.
The classical Adamjan-Arov-Krein (A-A-K) theorem relating the singular numbers of Hankel operators to best approximations of their symbols by rational functions is given an abstract version. This provides results for Hankel operators acting in weightedH
2(T; ), as well as inH
2(T
d
), and an A-A-K type extension of Sarason's interpolation theorem. In particular, it is shown that all compact Hankel operators inH
2(T
d
) are zero.Author partially supported by NSF grant DMS89-11717. 相似文献
18.
Liankuo Zhao 《Journal of Mathematical Analysis and Applications》2009,352(2):767-772
We study (small) Hankel operators on the Dirichlet space D with symbols in a class of function space, and show that such (small) Hankel operators are closely related to the corresponding Hankel operators on the Bergman space and the Hardy space H2. 相似文献
19.
刘永民 《数学物理学报(B辑英文版)》2000,20(1)
1IntroductionLetnbeaboundedsynunetricdomaininC"withBerg1llankernelK(z,w),fldenotestheEuclideanclosureofninCnandoflistheTopologicalboundaryWeassumethatnisinitsstandardrepresentationandthevolumemeasuredVofflisuormalized.Itfollowsfrom[1],[2]thatthekernelfullctionsK(-,.)havethespecialproperties:(l):K(O,w)=K(z,o)=l,z,wEfl;(2):K(z,w)/o1zEfl,wEfl;(3):.13hK(z,z)=oo;(4):K(z,w)-'isasmoothfunctiononC',xC".ofcourse,K(z,w)=K(w,z).Thecomplexcol1jugateoffisdenotedbyf.By5.7of[3]andpolarcoordinates,th… 相似文献