Open AccessBook
Combinatorial Matrix Theory
Richard A. Brualdi,H. J. Ryser +1 more
TLDR
In this paper, the existence theorems for combinatorially constrained matrices are given for instance matrices, digraphs, bigraphs and Latin squares, as well as some special graphs.Abstract:
1. Incidence matrices 2. Matrices and graphs 3. Matrices and digraphs 4. Matrices and bigraphs 5. Combinatorial matrix algebra 6. Existence theorems for combinatorially constrained matrices 7. Some special graphs 8. The permanent 9. Latin squares.read more
Citations
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Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics
TL;DR: To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree.
Book
Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory
TL;DR: This book brings together a vast body of results on matrix theory for easy reference and immediate application with hundreds of identities, inequalities, and matrix facts stated rigorously and clearly.
Journal ArticleDOI
Decentralized control of vehicle formations
TL;DR: It is proved that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that G has a rooted directed spanning tree.
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Which graphs are determined by their spectrum
Edwin van Dam,Willem H. Haemers +1 more
TL;DR: For almost all graphs the answer to the question in the title is still unknown as mentioned in this paper, and the cases for which the answer is known are surveyed in the survey of cases where the Laplacian matrix is known.
Book
Max-linear Systems: Theory and Algorithms
TL;DR: Max-algebra: Two Special Features.- One-sided Max-linear Systems and Max- algebraic Subspaces.
References
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Journal ArticleDOI
Matrices of zeros and ones with fixed row and column sum vectors
TL;DR: In this paper, the combinational properties of all m × n matrices of 0's and 1's having r i 1's in row i and s i 1s in column j were studied.
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The symbiotic relationship of combinatorics and matrix theory
TL;DR: In this paper, the authors demonstrate the mutually beneficial relationship that exists between combinatorics and matrix theory, and demonstrate the mutual benefit of combinatorial and matrix theoretic models.
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Strong Hall Matrices
TL;DR: In this article, the authors developed an inductive structure for nonsquare strong Hall matrices that is quite analogous to the well-known induction structure of square strong Hall (i.e., fully indecomposable) matrices.