Signatures, lifts, and eigenvalues of graphs

2014/12/21 by Shiping Liu, Liu, Shiping, Norbert Peyerimhoff +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #DNA and Nucleic Acid Chemistry #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #cs.DM #math.CO

paper · pdf · doi:10.48550/arxiv.1412.6841

12 pages, 3 figures

arxiv created 2014/12/21 · openalex publication_date 2014/12/21 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We study the spectra of cyclic signatures of finite graphs and the corresponding cyclic lifts. Starting from a bipartite Ramanujan graph, we prove the existence of an infinite tower of 3-cyclic lifts, each of which is again Ramanujan.

Citations

• Structural balance: a generalization of Heider's theory.
• Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees

Cited by

• On a magneto-spectral invariant on finite graphs

Related

• On the signed graphs with two distinct eigenvalues
• Spectra and eigenspaces of arbitrary lifts of graphs
• Spectra of lifted Ramanujan graphs
• Some regular signed graphs with only two distinct eigenvalues
• Interlacing Families I: Bipartite Ramanujan Graphs of All Degrees