  \textit{Minimum distance diagrams}, also known as
\textit{\textsf{L}--shapes}, have been used to study some properties related to
\textit{weighted Cayley digraphs} of \textit{degree} two and \textit{embedding
dimension three numerical semigroups}. In this particular case, it has been
shown that these discrete structures have at most two related
\textsf{L}--shapes. These diagrams are proved to be a good tool for studing
\textit{factorizations} and the \textit{catenary degree} for semigroups and
\textit{diameter} and \textit{distance} between vertices for digraphs.
