Abstract
For a connected graph, the first Zagreb eccentricity index (ξ1) is defined as the sum of the squares of the eccentricities of the vertices, and the second Zagreb eccentricity index (ξ2) is defined as the sum of the products of the eccentricities of pairs of adjacent vertices. We determine the n-vertex unicyclic graphs with minimum, second-minimum and third-minimum ξ1 and ξ2, the n-vertex unicyclic graphs with maximum and second-maximum ξ1, and the n-vertex unicyclic graphs with maximum, second-maximum and third-maximum ξ2.
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