# On the computational complexity of the Steiner k-eccentricity

The Steiner k-eccentricity of a vertex v of a graph G is the maximum Steiner distance over all k-subsets of V (G) which contain v. A linear time algorithm for calculating the Steiner k-eccentricity of a vertex on block graphs is presented. For general graphs, an O(n^ν(G)+1(n(G) + m(G) + k)) algorithm is designed, where ν(G) is the cyclomatic number of G. A linear algorithm for computing the Steiner 3-eccentricities of all vertices of a tree is also presented which improves the quadratic algorithm from [Discrete Appl. Math. 304 (2021) 181–195].

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