Interpolation theorem for the number of generalized end-vertices of spanning trees

The concept of end-vertex is generalized by defining the k-end-vertex, where the end-vertex of G is the 1-end-vertex of G. It is then proved that the number of k-end-vertices of spanning trees of a graph G has the interpolation property for every positive integer k. This is a generalization of S. Schuster's (1983) interpolation theorem.<
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