Graphs and matrices

  title={Graphs and matrices},
  author={Richard A. Brualdi and Bryan L. Shader and Lowell W. Beineke and Robin J. Wilson and Peter J. Cameron},
Null decomposition of trees
Algorithms and Discrete Applied Mathematics
Sketching for Data Streams and Numerical Linear Algebra: A Practical Guide to Model-Driven Algebra.
A study on resistance matrix of graphs
In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some
A formula for all minors of the adjacency matrix and an application
Abstract We supply a combinatorial description of any minor of the adjacency matrix of a graph. This descriptionis then used to give a formula for the determinant and inverse of the adjacency matrix,
Characterization of Cutsets in Networks With Application to Transient Stability Analysis of Power Systems
It is revealed that cutsets are intrinsically linked to cycles, another important concept in the graph theory, and an improved cutset index (ICI) is proposed based on these cutset properties that has better performance than the conventional cut set index especially in heavy-load cases.
N ov 2 01 7 Maximal determinants of combinatorial matrices
We prove that detA ≤ 6 n 6 whenever A ∈ {0, 1}n×n contains at most 2n ones. We also prove an upper bound on the determinant of matrices with the k-consecutive ones property, a generalisation of the
Computational and Analytical Tools for Resilient and Secure Power Grids
The vulnerability of power grids to cyber and physical attacks and failures is analyzed, efficient monitoring schemes for robust state estimation are designed, algorithms to control the grid under tension are developed, and methods to generate realistic power grid test cases are introduced.
On the Inverse of Bipartite Graphs with Unique Perfect Matchings and Reciprocal Eigenvalue Properties
The study of graph structures via different properties of its adjacency matrix is a widely studied subjects. Sometimes different structural properties of a graph get characterized by different
Machine Learning on Graphs
The contribution of this thesis is the derivation of the deterministic variational inference update equations for doing inference on the SHDPHMM, an improvement over the Markov Chain Monte Carlo algorithm proposed by Fox as it allows for direct assessment of convergence and can run faster.
Spectra of infinite graphs: two methods of computation
Two method for computation of the spectra of certain infinite graphs are suggested. The first one can be viewed as a reversed Gram--Schmidt orthogonalization procedure. It relies heavily on the