On the eccentricity energy of various graph products

The eccentricity matrix E(G) of a graph G is constructed from the distance matrix D(G) by only retaining the leading values in each row and each column and setting the rest of the elements in the corresponding row and column to zero. The paper aims to study the concepts of energy and the inertia of the eccentricity matrices of graphs obtained by means of various graph products, like the strong product, the Cartesian product and the Kronecker product, and well-established relations are derived in terms of their base graphs. Furthermore, we construct infinitely many pairs of non-isomorphic graphs having the same set of eigenvalues with respect to the eccentricity matrix.