International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 58, Pages 3657-3678
doi:10.1155/S0161171203302170
An algebraic framework of weighted directed graphs
Philippe Leroux
Institut de Recherche en Mathématiques de Rennes, Université de Rennes 1 et UMR 6625 CNRS, Campus de Beaulieu, Rennes Cedex 35042, France
Abstract
We show that an algebraic formulation of weighted directed graphs leads to introducing a k-vector space equipped with two coproducts Δ and Δ˜ verifying the so-called coassociativity breaking equation (Δ˜⊗id)Δ=(id⊗Δ)Δ˜. Such a space is called an L-coalgebra. Explicit examples of such spaces are constructed and links between graph theory and coassociative coalgebras are given.