Linear Representation of Graphs: Applications to Molecular Graphs

Ali Reza Ashrafi (1) , Alain Bretto (2) , Alain Faisant (3, 4)

1 University of Kashan (IRAN)
2 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
3 ICJ - Institut Camille Jordan
4 CTN - Combinatoire, théorie des nombres

In this article we build a linear representation starting from a multigraph; this allows us to give an algebraic view of the multi- graph we are studying. We show that two isomorphic multigraphs give equivalent representations ; conversely two equivalent represen- tations give isomorphic multigraphs. For the clarity of the article we give at the beginning, classical results on representations, never- theless these are specific to our graph representation.

Mots clés: linear representation of group; graph theory; mathematical chemistry

Domaines: Sciences de l'Homme et Société; Mathématiques [math]

Ali Reza Ashrafi, Alain Bretto, Alain Faisant. Linear Representation of Graphs: Applications to Molecular Graphs. MATCH Communications in Mathematical and in Computer Chemistry, In press, ⟨10.21203/rs.3.rs-2213289/v1⟩. ⟨hal-03940944⟩