Discrete Applied Mathematics, ISSN 0166-218X, 05/2017, Volume 223, pp. 1 - 14

In this paper, we study the spectra of weighted digraphs, where weights are taken from the set of non zero real numbers. We obtain formulae for the...

Coulson’s integral formula | Energy of a weighted digraph | Extremal energy | Spectrum of a weighted digraph | Bipartite weighted digraph | McClelland inequality | Coulson's integral formula | SIGNED DIGRAPHS | MATHEMATICS, APPLIED | GRAPHS

Coulson’s integral formula | Energy of a weighted digraph | Extremal energy | Spectrum of a weighted digraph | Bipartite weighted digraph | McClelland inequality | Coulson's integral formula | SIGNED DIGRAPHS | MATHEMATICS, APPLIED | GRAPHS

Journal Article

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Bipartite output synchronization of heterogeneous multiagent systems on signed digraphs

International Journal of Robust and Nonlinear Control, ISSN 1049-8923, 09/2018, Volume 28, Issue 13, pp. 4017 - 4031

Summary This paper studies the bipartite output synchronization problem of general linear heterogeneous multiagent systems on signed digraphs. We first show...

bipartite output synchronization | signed digraph | small‐gain theorem | heterogeneous multiagent systems | small-gain theorem | MATHEMATICS, APPLIED | CONSENSUS PROBLEMS | FEEDBACK CONTROL | NETWORKS | MODEL | ENGINEERING, ELECTRICAL & ELECTRONIC | DYNAMICS | CONVERGENCE | STATE-FEEDBACK | AGENTS | AUTOMATION & CONTROL SYSTEMS | State feedback | Multiagent systems | Computer simulation | Feedback control systems | Synchronism | Routing | Mathematical models | Graph theory | Internal model principle | Compensators | Output feedback

bipartite output synchronization | signed digraph | small‐gain theorem | heterogeneous multiagent systems | small-gain theorem | MATHEMATICS, APPLIED | CONSENSUS PROBLEMS | FEEDBACK CONTROL | NETWORKS | MODEL | ENGINEERING, ELECTRICAL & ELECTRONIC | DYNAMICS | CONVERGENCE | STATE-FEEDBACK | AGENTS | AUTOMATION & CONTROL SYSTEMS | State feedback | Multiagent systems | Computer simulation | Feedback control systems | Synchronism | Routing | Mathematical models | Graph theory | Internal model principle | Compensators | Output feedback

Journal Article

Algorithmica, ISSN 0178-4617, 10/2016, Volume 76, Issue 2, pp. 320 - 343

In the Directed Feedback Arc (Vertex) Set problem, we are given a digraph D with vertex set V(D) and arcs set A(D) and a positive integer k, and the question...

Feedback arc set | Feedback vertex set | Theory of Computation | Kernels | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Decomposable digraph | Locally semicomplete digraph | Computer Science | Bounded independence number | Quasi-transitive digraph | Algorithm Analysis and Problem Complexity | Parameterized complexity | SEMICOMPLETE DIGRAPHS | MATHEMATICS, APPLIED | NP | VERTEX SET | GRAPHS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ARC SET | BIPARTITE TOURNAMENTS | Computer science

Feedback arc set | Feedback vertex set | Theory of Computation | Kernels | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Decomposable digraph | Locally semicomplete digraph | Computer Science | Bounded independence number | Quasi-transitive digraph | Algorithm Analysis and Problem Complexity | Parameterized complexity | SEMICOMPLETE DIGRAPHS | MATHEMATICS, APPLIED | NP | VERTEX SET | GRAPHS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ARC SET | BIPARTITE TOURNAMENTS | Computer science

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2008, Volume 22, Issue 4, pp. 1624 - 1639

For digraphs D and H, a mapping f : V (D). V (H) is a homomorphism of D to H if uv is an element of A(D) implies f(u) f(v) is an element of A(H). If, moreover,...

Homomorphisms | Minimum cost homomorphisms | Semicomplete bipartite digraphs | homomorphisms | MATHEMATICS, APPLIED | minimum cost homomorphisms | semicomplete bipartite digraphs | DICHOTOMY | GRAPHS

Homomorphisms | Minimum cost homomorphisms | Semicomplete bipartite digraphs | homomorphisms | MATHEMATICS, APPLIED | minimum cost homomorphisms | semicomplete bipartite digraphs | DICHOTOMY | GRAPHS

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 05/2007, Volume 55, Issue 1, pp. 1 - 13

It is easily shown that every digraph with m edges has a directed cut of size at least m/4, and that 1/4 cannot be replaced by any larger constant. We...

maximum cut | directed cut | directed and acyclic graphs | extremal problems | Directed cut | Maximum cut | Extremal problems | Directed and acyclic graphs | MATHEMATICS | NUMBER | BIPARTITE SUBGRAPHS | GRAPHS

maximum cut | directed cut | directed and acyclic graphs | extremal problems | Directed cut | Maximum cut | Extremal problems | Directed and acyclic graphs | MATHEMATICS | NUMBER | BIPARTITE SUBGRAPHS | GRAPHS

Journal Article

ACM TRANSACTIONS ON ALGORITHMS, ISSN 1549-6325, 06/2018, Volume 14, Issue 2

Motivated by applications in cancer genomics and following the work of Hajirasouliha and Raphael (WABI 2014), Hujdurovic et al. (IEEE TCBB, 2018) introduced...

MATHEMATICS, APPLIED | BIPARTITE | min-max theorem | minimum conflict-free row split problem | APPROXIMATION | Perfect phylogeny | chain partition | APX-hardness | ALGORITHMS | branching | Dilworth's theorem | GRAPHS | TREES | COMPLEXITY | approximation algorithm | COMPUTER SCIENCE, THEORY & METHODS | acyclic digraph

MATHEMATICS, APPLIED | BIPARTITE | min-max theorem | minimum conflict-free row split problem | APPROXIMATION | Perfect phylogeny | chain partition | APX-hardness | ALGORITHMS | branching | Dilworth's theorem | GRAPHS | TREES | COMPLEXITY | approximation algorithm | COMPUTER SCIENCE, THEORY & METHODS | acyclic digraph

Journal Article

International Journal of Systems Science, ISSN 0020-7721, 10/2016, Volume 47, Issue 13, pp. 3116 - 3131

In this paper, we concentrate on investigating bipartite output consensus in networked multi-agent systems of high-order power integrators. Systems with power...

signed digraph | Bipartite output consensus | input noises | networked multi-agent systems | power integrator | high-order | TOPOLOGIES | STABILIZATION | INFORMATION | COORDINATION | COMMUNICATION NOISES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONLINEAR-SYSTEMS | ANTAGONISTIC INTERACTIONS | AGENTS | COMPUTER SCIENCE, THEORY & METHODS | AUTOMATION & CONTROL SYSTEMS | COOPERATIVE CONTROL | Adaptive systems | Multiagent systems | Noise | Deterioration | Reagents | Graph theory | Integrators | Compensators

signed digraph | Bipartite output consensus | input noises | networked multi-agent systems | power integrator | high-order | TOPOLOGIES | STABILIZATION | INFORMATION | COORDINATION | COMMUNICATION NOISES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONLINEAR-SYSTEMS | ANTAGONISTIC INTERACTIONS | AGENTS | COMPUTER SCIENCE, THEORY & METHODS | AUTOMATION & CONTROL SYSTEMS | COOPERATIVE CONTROL | Adaptive systems | Multiagent systems | Noise | Deterioration | Reagents | Graph theory | Integrators | Compensators

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 5/1998, Volume 7, Issue 3, pp. 285 - 290

Let G be a bipartite graph with a bicoloration {A,B}, |A|=|B|. Let E(G) → A x B denote the edge set of G, and let m(G) denote the number of perfect matchings...

group algebra | digraph | Olson's Theorem | Convex and Discrete Geometry | finite abelian group | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | bipartite matching | Group algebra | Bipartite matching | Digraph | Finite abelian group | MATHEMATICS | FAMILIES | Algebra

group algebra | digraph | Olson's Theorem | Convex and Discrete Geometry | finite abelian group | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | bipartite matching | Group algebra | Bipartite matching | Digraph | Finite abelian group | MATHEMATICS | FAMILIES | Algebra

Journal Article

BMC Systems Biology, ISSN 1752-0509, 02/2014, Volume 8, Issue 1, pp. 22 - 22

Background: A biochemical mechanism with mass action kinetics can be represented as a directed bipartite graph (bipartite digraph), and modeled by a system of...

Oscillations | Multistability | Parameter-free model discrimination | Biochemical mechanism | Bipartite digraph | Turing instability | COMPLEX ISOTHERMAL REACTORS | INJECTIVITY | PATTERN-FORMATION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | CHEMICAL-REACTION NETWORKS | MULTIPLE EQUILIBRIA | Computer Graphics | Linear Models | Computational Biology - methods | Kinetics | Models | Public software | Differential equations | Mathematical models | Algorithms | Research parks | Equilibrium | Methods

Oscillations | Multistability | Parameter-free model discrimination | Biochemical mechanism | Bipartite digraph | Turing instability | COMPLEX ISOTHERMAL REACTORS | INJECTIVITY | PATTERN-FORMATION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | CHEMICAL-REACTION NETWORKS | MULTIPLE EQUILIBRIA | Computer Graphics | Linear Models | Computational Biology - methods | Kinetics | Models | Public software | Differential equations | Mathematical models | Algorithms | Research parks | Equilibrium | Methods

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 2006, Volume 96, Issue 5, pp. 673 - 683

A bipartite graph is chordal bipartite if it does not contain an induced cycle of length at least six. We give three representation characterizations of...

Characterization | Chordal bipartite graph | Strongly chordal graph | Interval bigraph | Circular arc graph | Ferrers dimension | INTERVAL-GRAPHS | MATHEMATICS | LIST HOMOMORPHISMS | chordal bipartite graph | interval bigraph | circular arc graph | strongly chordal graph | CIRCULAR-ARC GRAPHS | DIGRAPHS | characterization

Characterization | Chordal bipartite graph | Strongly chordal graph | Interval bigraph | Circular arc graph | Ferrers dimension | INTERVAL-GRAPHS | MATHEMATICS | LIST HOMOMORPHISMS | chordal bipartite graph | interval bigraph | circular arc graph | strongly chordal graph | CIRCULAR-ARC GRAPHS | DIGRAPHS | characterization

Journal Article

SIAM JOURNAL ON DISCRETE MATHEMATICS, ISSN 0895-4801, 05/1993, Volume 6, Issue 2, pp. 270 - 273

A digraph obtained by replacing each edge of a complete m-partite graph with an arc or a pair of mutually opposite arcs with the same end vertices is called a...

DIGRAPH | MATHEMATICS, APPLIED | LONGEST PATH | POLYNOMIAL ALGORITHM | BIPARTITE TOURNAMENTS | CYCLES

DIGRAPH | MATHEMATICS, APPLIED | LONGEST PATH | POLYNOMIAL ALGORITHM | BIPARTITE TOURNAMENTS | CYCLES

Journal Article

SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2007, Volume 29, Issue 2, pp. 554 - 565

An m by n sign pattern S is an m by n matrix with entries in {+,-, 0}. Such a sign pattern allows a positive (resp., nonnegative) left inverse, provided that...

Bipartite digraph | Positive left inverse | Positive left null-vector | Sign pattern | Nonnegative left inverse | Strong hall | sign pattern | nonnegative left inverse | MATHEMATICS, APPLIED | positive left null-vector | MATRICES | strong Hall | bipartite digraph | positive left inverse

Bipartite digraph | Positive left inverse | Positive left null-vector | Sign pattern | Nonnegative left inverse | Strong hall | sign pattern | nonnegative left inverse | MATHEMATICS, APPLIED | positive left null-vector | MATRICES | strong Hall | bipartite digraph | positive left inverse

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 11/2018, Volume 63, Issue 11, pp. 3881 - 3888

This paper addresses optimal feedback selection for arbitrary pole placement of structured systems when each feedback edge is associated with a cost. Given a...

linear output feedback | minimum cost control selection | Arbitrary pole placement | Heuristic algorithms | Approximation algorithms | Bipartite graph | Dynamic programming | Topology | Closed loop systems | Output feedback | linear structured systems | Linear structured systems | Linear output feedback | Minimum cost control selection | FIXED MODES | PATTERNS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Placement | Feedback | Minimum cost | Graph theory | Pole placement | Polynomials | Time constant | Cost engineering | Graph matching

linear output feedback | minimum cost control selection | Arbitrary pole placement | Heuristic algorithms | Approximation algorithms | Bipartite graph | Dynamic programming | Topology | Closed loop systems | Output feedback | linear structured systems | Linear structured systems | Linear output feedback | Minimum cost control selection | FIXED MODES | PATTERNS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Placement | Feedback | Minimum cost | Graph theory | Pole placement | Polynomials | Time constant | Cost engineering | Graph matching

Journal Article

IEICE Transactions on Information and Systems, ISSN 0916-8532, 2018, Volume E101.D, Issue 3, pp. 611 - 612

Given an edge-weighted bipartite digraph G=(A,B;E), the Bipartite Traveling Salesman Problem (BTSP) asks to find the minimum cost of a Hamiltonian cycle of G,...

Stirling's formula | exact algorithms | polynomial space | bipartite traveling salesman problem | divide-and-conquer | Bipartite traveling salesman problem | Polynomial space | Divide-and-conquer | Exact algorithms | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, INFORMATION SYSTEMS | Minimum cost | Graphs | Traveling salesman problem | Graph theory | Polynomials | Algorithms

Stirling's formula | exact algorithms | polynomial space | bipartite traveling salesman problem | divide-and-conquer | Bipartite traveling salesman problem | Polynomial space | Divide-and-conquer | Exact algorithms | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, INFORMATION SYSTEMS | Minimum cost | Graphs | Traveling salesman problem | Graph theory | Polynomials | Algorithms

Journal Article

Complexity, ISSN 1076-2787, 9/2019, Volume 2019, pp. 1 - 13

In this paper, the concept of consensus is generalized to weighted consensus, by which the conventional consensus, the bipartite consensus, and the cluster...

TRACKING CONTROL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | CLUSTER SYNCHRONIZATION | STATE-FEEDBACK | AGENTS | BIPARTITE CONSENSUS | OBSERVER | COMPLEX NETWORKS | State feedback | Multiagent systems | Time invariant systems | Clusters | Graphs | Graph theory | Feedback control | Topology | Output feedback

TRACKING CONTROL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | CLUSTER SYNCHRONIZATION | STATE-FEEDBACK | AGENTS | BIPARTITE CONSENSUS | OBSERVER | COMPLEX NETWORKS | State feedback | Multiagent systems | Time invariant systems | Clusters | Graphs | Graph theory | Feedback control | Topology | Output feedback

Journal Article

Lecture Notes in Electrical Engineering, ISSN 1876-1100, 2019, Volume 528, pp. 339 - 349

Conference Proceeding

Mathematical Problems in Engineering, ISSN 1024-123X, 10/2018, Volume 2018, pp. 1 - 14

In this paper, the optimal topology structure is studied for hybrid-weighted leader-follower multiagent systems (MASs). The results are developed by taking...

EQUILIBRIUM TOPOLOGY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SUFFICIENT CONDITIONS | NETWORKS | BIPARTITE CONSENSUS | SELECTION | CONTROLLABILITY | STATE ESTIMATION | Cost control | Leadership | Multiagent systems | Hybrid systems | Topology | Composite structures | Followers | Phase transitions | Linear quadratic regulator | Cybernetics

EQUILIBRIUM TOPOLOGY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SUFFICIENT CONDITIONS | NETWORKS | BIPARTITE CONSENSUS | SELECTION | CONTROLLABILITY | STATE ESTIMATION | Cost control | Leadership | Multiagent systems | Hybrid systems | Topology | Composite structures | Followers | Phase transitions | Linear quadratic regulator | Cybernetics

Journal Article

International Journal of Control, ISSN 0020-7179, 04/2018, Volume 91, Issue 4, pp. 827 - 847

This paper aims at solving convergence problems on directed signed networks with multiple nodes, where interactions among nodes are described by signed...

(interval) bipartite consensus | digon sign-(un)symmetry | stability | M-matrices | structural (un)balance | Directed signed networks | OUTPUT-FEEDBACK CONTROL | PROTOCOLS | OPINION DYNAMICS | MULTIAGENT SYSTEMS | COORDINATION | STRATEGIES | BIPARTITE CONSENSUS | FINITE-TIME CONSENSUS | BEHAVIORS | AUTOMATION & CONTROL SYSTEMS | Networks | Graph theory | Mathematical analysis | Matrix methods | Convergence

(interval) bipartite consensus | digon sign-(un)symmetry | stability | M-matrices | structural (un)balance | Directed signed networks | OUTPUT-FEEDBACK CONTROL | PROTOCOLS | OPINION DYNAMICS | MULTIAGENT SYSTEMS | COORDINATION | STRATEGIES | BIPARTITE CONSENSUS | FINITE-TIME CONSENSUS | BEHAVIORS | AUTOMATION & CONTROL SYSTEMS | Networks | Graph theory | Mathematical analysis | Matrix methods | Convergence

Journal Article

Asian Journal of Control, ISSN 1561-8625, 01/2018, Volume 20, Issue 1, pp. 577 - 584

The bipartite consensus problem is investigated for double‐integrator multi‐agent systems in the presence of measurement noise. A distributed protocol with...

multi‐agent systems | double‐integrator | measurement noise | Bipartite linear χ‐consensus | multi-agent systems | Bipartite linear χ-consensus | double-integrator

multi‐agent systems | double‐integrator | measurement noise | Bipartite linear χ‐consensus | multi-agent systems | Bipartite linear χ-consensus | double-integrator

Journal Article

Cybernetics and Systems Analysis, ISSN 1060-0396, 9/2016, Volume 52, Issue 5, pp. 748 - 757

The well-known problem of weighted matching in an arbitrary graph H with n vertices is reduced to a matching problem for a bipartite graph with 2n vertices....

Processor Architectures | Systems Theory, Control | Artificial Intelligence (incl. Robotics) | Software Engineering/Programming and Operating Systems | assignment problem | weighted matching problem | Mathematics | bipartite graph | augmenting path | matching | Algorithms | Studies | Graph theory | Polynomials | Mathematical analysis | Matching | Graphs | Systems analysis | Order disorder | Cybernetics | Graph matching

Processor Architectures | Systems Theory, Control | Artificial Intelligence (incl. Robotics) | Software Engineering/Programming and Operating Systems | assignment problem | weighted matching problem | Mathematics | bipartite graph | augmenting path | matching | Algorithms | Studies | Graph theory | Polynomials | Mathematical analysis | Matching | Graphs | Systems analysis | Order disorder | Cybernetics | Graph matching

Journal Article

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