Taking into account relationships between interacting objects can improve the understanding of the dynamic model governing their behaviors. Moreover, maintaining a belief about the ongoing activity while tracking allows ...

We establish the bounds 4 on the Nordhaus- Gaddum sum upper bound multipliers for all graphs G, in connections with certain Colin de Verdi ere type graph parameters. The Nordhaus-Gaddum sum lower bound is conjectured ...

Fire Blight is a destructive disease of apple and pear caused by the enteric bacterial pathogen, Erwinia amylovora. E. amylovora initiates infection by colonizing the stigmata of apple and pear trees, and entering the ...

The positive semidefinite zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring and is related to a more conventional version of zero forcing. We establish a relation ...

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 ...

Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all ...

The Colin de Verdi`ere parameters mu and nu are defined to be the maximum nullity of certain real symmetric matrices associated with a given graph. In this work, both of these parameters are calculated for all chordal ...

In this work, we study the structure of the null spaces of matrices associated with graphs. Our primary tool is utilizing Schur complements based on certain collections of independent vertices. This idea is applied in ...

Tree-width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the ...