4 papers · 1 filter
Adjacency Spectral Radius Under Laplacian Sparsification: Deterministic and Probabilistic Bounds
Joshua Steier
Spielman-Srivastava spectral sparsification preserves Laplacian quadratic forms to within (1 +/- epsilon), but does not directly control the adjacency spectral radius lambda_1, whi…
Spectral and Homological Bounds on k-Component Edge Connectivity
Joshua Steier
We present a novel theoretical framework connecting k-component edge connectivity with spectral graph theory and homology theory to pro vide new insights into the resilience of rea…
On the Degree Sequences of Multigraphs with Edge Additions and Deletions
Joshua Steier
The degree sequence of a graph is a numerical method to characterize the properties of graphs. Generalized forms of degree sequences exist for complete graphs and complete graphs.…
A Characterization of Distance Matrices of Positive Weighted Kneser Graphs and Generalized Petersen Graphs
Joshua Steier, Luis Monterroso
Rubei et. al., established results for the distance matrix of positive weighted Petersen graphs. Focusing on the properties of the distance matrix, we generalized positive weighted…