Using twins and scaling to construct cospectral graphs for the normalized Laplacian

2014/09/29 by Steve Butler, Butler, Steve
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #math.CO

paper · pdf · doi:10.48550/arxiv.1409.8329

openalex publication_date 2014/09/29 · arxiv created 2014/10/23 · arxiv updated 2014/10/27 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The spectrum of the normalized Laplacian matrix cannot determine the number of edges in a graph, however finding constructions of cospectral graphs with differing number of edges has been elusive. In this paper we use basic properties of twins and scaling to show how to construct such graphs. We also give examples of families of graphs which are cospectral with a subgraph for the normalized Laplacian matrix.

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