Integer Index in Trees of Diameter 4

Laura Patuzzi, Maria Aguieiras A. de Freitas, Renata R. Del-Vecchio

We characterize when a tree of diameter 4 has integer index and we provide examples of infinite families of non-integral trees with integer index. We also determine a tight upper bound for the index of any tree of diameter 4 based on its maximum degree. Moreover, we present a new infinite family of integral trees of diameter 4.