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81.
This paper is a survey of reachability and controllability results for discrete-time positive linear systems. It presents a variety of criteria in both algebraic and digraph forms for recognising these fundamental system properties with direct implications not only in dynamic optimization problems (such as those arising in inventory and production control, manpower planning, scheduling and other areas of operations research) but also in studying properties of reachable sets, in feedback control problems, and others. The paper highlights the intrinsic combinatorial structure of reachable/controllable positive linear systems and reveals the monomial components of such systems. The system matrix decomposition into monomial components is demonstrated by solving some illustrative examples. 相似文献
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In 2006, Sullivan stated the conjectures:(1) every oriented graph has a vertex x such that d~(++)(x) ≥ d~-(x);(2) every oriented graph has a vertex x such that d~(++)(x) + d~+(x) ≥ 2 d~-(x);(3) every oriented graph has a vertex x such that d~(++)(x) + d~+(x) ≥ 2 · min{d~+(x), d~-(x)}. A vertex x in D satisfying Conjecture(i) is called a Sullivan-i vertex, i = 1, 2, 3. A digraph D is called quasi-transitive if for every pair xy, yz of arcs between distinct vertices x, y, z, xz or zx("or" is inclusive here) is in D. In this paper, we prove that the conjectures hold for quasi-transitive oriented graphs, which is a superclass of tournaments and transitive acyclic digraphs. Furthermore, we show that a quasi-transitive oriented graph with no vertex of in-degree zero has at least three Sullivan-1 vertices and a quasi-transitive oriented graph has at least three Sullivan-3 vertices unless it belongs to an exceptional class of quasitransitive oriented graphs. For Sullivan-2 vertices, we show that an extended tournament, a subclass of quasi-transitive oriented graphs and a superclass of tournaments, has at least two Sullivan-2 vertices unless it belongs to an exceptional class of extended tournaments. 相似文献
84.
In this paper, D=(V(D),A(D)) denotes a loopless directed graph (digraph) with at most one arc from u to v for every pair of vertices u and v of V(D). Given a digraph D, we say that D is 3-quasi-transitive if, whenever u→v→w→z in D, then u and z are adjacent or u=z. In Bang-Jensen (2004) [3], Bang-Jensen introduced 3-quasi-transitive digraphs and claimed that the only strong 3-quasi-transitive digraphs are the strong semicomplete digraphs and strong semicomplete bipartite digraphs. In this paper, we exhibit a family of strong 3-quasi-transitive digraphs distinct from strong semicomplete digraphs and strong semicomplete bipartite digraphs and provide a complete characterization of strong 3-quasi-transitive digraphs. 相似文献
85.
A k‐king in a digraph D is a vertex which can reach every other vertex by a directed path of length at most k. We consider k‐kings in locally semicomplete digraphs and mainly prove that all strong locally semicomplete digraphs which are not round decomposable contain a 2‐king. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 279–287, 2010 相似文献
86.
W. Mader 《Journal of Graph Theory》2010,63(2):93-105
We deal with conditions for a digraph of minimum degree r which imply the existence of a vertex x contained in r circuits which have pairwise only x in common. In particular, we give some positive answers to a question of P. Seymour, whether an r‐regular digraph has a vertex x which is contained in r circuits pairwise disjoint except for x, and show that the answer, in general, is negative. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 93–105, 2010 相似文献
87.
XuJunming FanYingmei 《高校应用数学学报(英文版)》2004,19(4):449-454
The super edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks. This note shows that the Kautz undirected graph is super edge-connected,and provides a short proof of Lue and Zhang‘s result on super edge-connectivity of the de Bruijn undirected graph. 相似文献
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Meng Jixiang 《新疆大学学报(理工版)》1996,(3)
IsomorphismsofCayleyDigraphsofInfiniteAbelianGroups¥MengJixiang(DepartmentofMathematics,XinjiangUniversity,Urumchi,830046)Abs... 相似文献