Integral trees with diameters 5 and 6

Abstract: In this paper, some new families of integral trees with diameters 5 and 6 are constructed. All these classes are infinite. These are different from those in the existing literature. We also prove that the problem of finding integral trees of diameters 5 and 6 is equivalent to the problem of solving some Diophantine equations. The discovery of these integral trees is a new contribution to the search for such trees. [Copyright &y& Elsevier]