Extremizing algebraic connectivity subject to graph theoretic constraints.
On the Cayley transform of positivity classes of matrices.
On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices.
A variant on the graph parameters of Colin de Verdière: implications to the minimum rank of graphs.
Multiplicative principal-minor inequalities for a class of oscillatory matrices.
On matrices with all minors negative.
The general totally positive matrix completion problem with few unspecified entries.
Minimum semidefinite rank of outerplanar graphs and the tree cover number.
Line graphs: their maximum nullities and zero forcing numbers
The maximum nullity over a collection of matrices associated with a graph has been attracting the attention of numerous researchers for at least three decades. Along these lines various zero forcing parameters have been devised and utilized for bounding the maximum nullity. The maximum nullity and zero forcing number, and their positive counterparts, for general families of line graphs associated with graphs possessing a variety of specific properties are analysed. Building upon earlier work, where...
On the minimum rank of not necessarily symmetric matrices: a preliminary study.
On the Relationships between Zero Forcing Numbers and Certain Graph Coverings
The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all the vertices of the graph, while the positive zero forcing number is an upper bound on the minimum number of induced trees in the graph needed to cover all the vertices in the graph. We show that for a block-cycle graph the zero forcing number equals...
Editors’ Summary of the Special Issue dedicated to the 5th International Conference on Matrix Analysis and Applications
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