Reconfiguration of Graph Colorings

For this thesis, we consider two $k$-colorings of a graph $G$ adjacent if one can recolor one into the other by changing the color of one vertex. The reconfiguration graph of a graph $G$ on $k$ colors $\mathcal{C}_{k}(G)$ is the graph for which the vertices are the $k$-colorings of $G$, and an edge is between two $k$-colorings if they are...

Weighted Betweenness and Algebraic Connectivity

One of the better studied topology metrics of complex networks is the second smallest eigenvalue of the Laplacian matrix of a network’s graph, referred to as the algebraic connectivity mN-1. This spectral metric plays a decisive role in synchronization of coupled oscillators, network robustness, consensus problems, belief propagation, graph...

The Imperfection Data Bank and its Applications

Imperfections are irregularities of the shape of a thin-walled shell, such as those used for rocket structures or silos. Knowing the imperfections is very important as thin-walled shells are very sensitive to imperfections. Even a small deviation with respect to the perfect shell shape reduces the buckling load significantly. The main objective...