On the graphs having at most one positive eccentricity eigenvalue

2020/12/20 by Sezer Sorgun, Sorgun, Sezer, Hakan Küçük +1
Computer Science · Mathematics · #05C05 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2012.10933

openalex publication_date 2020/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The eccentricity (anti-adjacency) matrix ε(G) of a graph G is obtained from the distance matrix by retaining the eccentricities in each row and each column. This matrix is first defined in 2018 by Wang et al. \cite1. In this paper we have characterized the graphs which have at most one (hence exactly) positive eigenvalue of ε(G).

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