Spectrum of Laplacians for Graphs with Self-Loops

Behcet Acikmese

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arXiv · 1505.08133

Spectrum of Laplacians for Graphs with Self-Loops

Behcet Acikmese

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Abstract

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.

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Behcet Acikmese. 2015-05-29. Spectrum of Laplacians for Graphs with Self-Loops. https://arxiv.org/abs/1505.08133

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