  Let $n$ be a nonnegative integer, we use ribbon $n-$graph diagrams and the
Yamada polynomial skein relations to construct an algebra ${\mathcal Y}_n$
which is shown to be closely related to the Temerley-Lieb Algebra. We prove
that the algebra ${\mathcal Y}_2$ is isomorphic to some quotient of a three
variables polynomial algebra. Then, we give a family of generators for the
algebra ${\mathcal Y}_3$.
