Vertex Centers of Trees

A unified theoretical basis for a class of vertex centers of trees is presented. A general algorithm for determining such vertex centers is defined and proved to be correct. A linear (in both time and space) implementation of the algorithm is specified in a FORTRAN-like code. A leaf-determined representation of trees is introduced. This representation makes possible the linear time property of the implementation. Two notions of tree center that fall outside the domain of the algorithm are discussed.