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} $Gut(J^*_{ n+1}(x)).$ We also determine the \emph{ Gutman index} for the trivial \emph{ edge-joint} between Jaco graphs.
Categories: math.CO