Abstract
AbstractThe Steiner distance of a set S of vertices in a connected graph G is the minimum size among all connected subgraphs of G containing S. For n ≥ 2, the n‐eccentricity en(ν) of a vertex ν of a graph G is the maximum Steiner distance among all sets S of n vertices of G that contains ν. The n‐diameter of G is the maximum n‐eccentricity among the vertices of G while the n‐radius of G is the minimum n‐eccentricity. The n‐center of G is the subgraph induced by those vertices of G having minimum n‐eccentricity. It is shown that every graph is the n‐center of some graph. Several results on the n‐center of a tree are established. In particular, it is shown that the n‐center of a tree is a tree and those trees that are n‐centers of trees are characterized.
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