The spectra of the complements of graphs with given connectivity

2022/09/13 by Huan Qiu, Qiu, Huan, Keng Li +3
Computer Science · Mathematics · Physics and Astronomy · #05C12 #05C50 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2209.05694

openalex publication_date 2022/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spectral radius of a graph G is the largest eigenvalue of adjacency matrix of G. The least eigenvalue of a graph G is the least eigenvalue of adjacency matrix of G. In this paper we determine the graphs which attain respectively the minimum spectral radius and the minimum least eigenvalue among all complements of connected simple graphs with given connectivity. Spectral radius of a graph G is the largest eigenvalue of adjacency matrix of G. The least eigenvalue of a graph G is the least eigenvalue of adjacency matrix of G. In this paper we determine the graphs which attain respectively the minimum spectral radius and the minimum least eigenvalue among all complements of connected simple graphs with given connectivity.

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