Determination of large families and diameter of equiseparable trees

Abstract

We consider the problem of determining all the members of an arbitrary family of equiseparable trees. We introduce the concept of saturation (based on the number partitions). After that, we use the same concept to obtain the least upper bound for the difference in the diameters of two equiseparable trees with m edges. We prove that this bound is equal to $(m-4)/3$, where $m$ is the size of trees.