Linear Representation of Graphs: Applications to Molecular Graphs

In this article we build a linear representation starting from a multigraph; this allows us to give an algebraic view of the multigraph we are studying. We show that two isomorphic multigraphs give equivalent representations; conversely two equivalent representations give isomorphic multigraphs. For the clarity of the article we give at the beginning, classical results on representations, nevertheless these are specific to our graph representation.