Abstract
The eccentricity matrix [Formula: see text] of a graph [Formula: see text] is constructed from the distance matrix by keeping each row and each column only the largest distances with [Formula: see text] where [Formula: see text] is the distance between two vertices [Formula: see text] and [Formula: see text], and [Formula: see text] is the eccentricity of the vertex [Formula: see text]. The [Formula: see text]-eigenvalues of [Formula: see text] are those of its eccentricity matrix. In this paper, employing the well-known Cauchy Interlacing Theorem we give the following lower bounds for the second, the third and the fourth largest [Formula: see text]-eigenvalues by means of the diameter [Formula: see text] of [Formula: see text]: [Formula: see text] where [Formula: see text] is the second largest root of [Formula: see text]. Moreover, we further discuss the graphs achieving the above lower bounds.
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