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
Institut de Recherche en Mathématiques de Rennes, Université de Rennes 1 et UMR 6625 CNRS, Campus de Beaulieu, Rennes Cedex 35042, France
Received 19 February 2003
Copyright © 2003 Philippe Leroux. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.