For an element $r$ of a ring $R$, Diophantine $D(r)$ $m$-tuple is $(a_1,a_2,\ldots,a_m)$ elements $R$ such that for all $i,j$ with $i\neq j$, $a_ia_j+r$ perfect square in $R$. In this article, we compute and estimate the measures sets $m$-tuples $\mathbb{Z}_p$ $p$-adic integers, as well its residue field $\mathbb{F}_p$.

the harary index h can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms, such that their magnitude decreases with the increasing distance between the respective two atoms. a generalization of the harary index, denoted by hk, is achieved by employing the steiner-type distance between k-tuples of atoms. we show that the linear c...