A lower bound for the smallest eigenvalue of a graph and an application to the associahedron graph

2022/10/16 by Sebastian M. Cioabă, Vishal Gupta, Cioabă, Sebastian M. +1
Computer Science · Mathematics · Neuroscience · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Nuclear Receptors and Signaling

paper · pdf · doi:10.48550/arxiv.2210.08516

openalex publication_date 2022/10/16 · openalex created_date 2022/10/20 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain a lower bound for the smallest eigenvalue of a regular graph containing many copies of a smaller fixed subgraph. This generalizes a result of Aharoni, Alon, and Berger in which the subgraph is a triangle. We apply our results to obtain a lower bound on the smallest eigenvalue of the associahedron graph, and we prove that this bound gives the correct order of magnitude of this eigenvalue. We also survey what is known regarding the second-largest eigenvalue of the associahedron graph.

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