نتایج جستجو برای: directed graph

تعداد نتایج: 337759  

2003
CHRISTOS A. ATHANASIADIS

The Laplacian of a directed graph G is the matrix L(G) = 0(G) — A(G), where A(G) is the adjacency matrix of G and O(G) the diagonal matrix of vertex outdegrees. The eigenvalues of G are the eigenvalues of A(G). Given a directed graph G we construct a derived directed graph D(G) whose vertices are the oriented spanning trees of G. Using a counting argument, we describe the eigenvalues of D(G) an...

Journal: :Journal of Graph Theory 2015
Gábor Simonyi Gábor Tardos Ambrus Zsbán

The local chromatic number is a coloring parameter defined as the minimum number of colors that should appear in the most colorful closed neighborhood of a vertex under any proper coloring of the graph. Its directed version is the same when we consider only outneighborhoods in a directed graph. For digraphs with all arcs being present in both directions the two values are obviously equal. Here ...

Journal: :Australasian J. Combinatorics 1993
N. R. Achuthan Lou Caccetta

The simplest way to overcome the problem is to change formulation. Recall that in [1] we extended the given directed graph G* with one source (s) and two sinks slightly the graph G to a (t and t ). 1 2 Further, our formulation restricted the out degree of the source s to one. Here we modify the directed graph by allowing only one sink et) and restricting the out degree of the source s to at mos...

2007
Damir Dzhafarov

Example 3.1.4. Let G be a directed graph and suppose vertex v has indegree k and outdegree `, i. e., k edges end at v and ` edges start at v. Each of these k+ ` edges will represent a vertex in the directed line graph ~ L(G), and since the terminus of each of the former k edges is the initial point of each of the latter `, in the line graph each of the former will have an edge directing to each...

ژورنال: کنترل 2022

In this paper, the design of a distributed adaptive controller for a class of unknown non-affine MIMO strict-feedback multi agent systems with time delay has been performed under a directed graph. The controller design is based on dynamic surface control  method. In the design process, radial basis function neural networks (RBFNNs) were employed to approximate the unknown nonlinear functions. S...

Journal: :Journal of Graph Theory 1997
Christos A. Athanasiadis

The branching operation D, defined by Propp, assigns to any directed graph G another directed graph D(G) whose vertices are the oriented rooted spanning trees of the original graph G. We characterize the directed graphs G for which the sequence δ(G) = (G,D(G), D(G), . . .) converges, meaning that it is eventually constant. As a corollary of the proof we get the following conjecture of Propp: fo...

Journal: :Theor. Comput. Sci. 2006
Venkatesh Raman Saket Saurabh

The parameterized feedback vertex (arc) set problem is to find whether there are k vertices (arcs) in a given graph whose removal makes the graph acyclic. The parameterized complexity of this problem in general directed graphs is a long standing open problem. We investigate the problems on tournaments, a well studied class of directed graphs. We consider both weighted and unweighted versions. W...

Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...

Journal: :Electronic Notes in Discrete Mathematics 2009
Michel Habib Juraj Stacho

The directed vertex leafage of a chordal graph G is the smallest integer k such that G is the intersection graph of subtrees of a rooted directed tree where each subtree has at most k leaves. In this note, we show how to find in time O(kn) an optimal colouring, a maximum independent set, a maximum clique, and an optimal clique cover of an n-vertex chordal graph G with directed vertex leafage k ...

2009
Leslie Hogben

A graph describes the zero-nonzero pattern of a family of matrices, with the type of graph (undirected or directed, simple or allowing loops) determining what type of matrices (symmetric or not necessarily symmetric, diagonal entries free or constrained) are described by the graph. The minimum rank problem of the graph is to determine the minimum among the ranks of the matrices in this family; ...

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