A Note on the Gutman Index of Jaco Graphs

The concept of the \emph{Gutman index}, denoted $Gut(G)$ was introduced for a connected undirected graph $G$. In this note we apply the concept to the underlying graphs of the family of Jaco graphs, (\emph{directed graphs by definition}), and describe a recursive formula for the \emph{Gutman index} $Gut(J_{n+1}^{\ast }(x))\mathrm{.}$ We also determine the \emph{Gutman index} for the trivial \emph{edge-joint} between Jaco graphs.