Abstract
The eccentricity matrix of a digraph is obtained from the distance matrix by keeping the largest distances in each row and each column, and leaving 0 in the remaining ones. Randić (2013) first defined D MAX -matrix of a graph and renamed it as eccentricity matrix by Wang et al. (2018). In this paper, we extend the concept of the eccentricity matrix of a graph to a digraph. We consider the irreducibility of the eccentricity matrix of a digraph with diameter 2 and obtain the lower bounds of ɛ -energy of a digraph with diameter 2. We characterize the lower bound of the spectral radius of the eccentricity matrix of a digraph and the corresponding extremal digraphs. Moreover, we give the ɛ -spectra and ɛ -energies of some digraphs.
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