2015/05/29 by Acikmese, Behcet
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1505.08133
This note introduces a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of undirected graphs with self-loops. We extend on the known results for the spectrum of undirected graphs without self-loops or multiple edges. For this purpose, we introduce a new concept of pseudo-connected graphs and apply a lifting of the graph with self-loops to a graph without self-loops, which is then used to quantify the spectrum of the Laplacian for the graph with self-loops.