On the least distance eigenvalue of a graph

Abstract Denote by D ( G ) = ( d i , j ) n × n the distance matrix of a connected graph G with n vertices, where d i j is equal to the distance between vertices v i and v j in G. The least eigenvalue of D ( G ) is called the least distance eigenvalue of G, denoted by λ n . In this paper, we determine all the graphs with λ n ∈ [ − 2.383 , 0 ] .