On the graphs having at most one positive eccentricity eigenvalue

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. [1].In this paper we have characterized the graphs which have at most one (hence exactly) positive eigenvalue of ε(G).