International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 406523 | https://doi.org/10.1155/S0161171203302170

Philippe Leroux, "An algebraic framework of weighted directed graphs", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 406523, 22 pages, 2003. https://doi.org/10.1155/S0161171203302170

An algebraic framework of weighted directed graphs

Received19 Feb 2003

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=(idΔ)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.

Copyright © 2003 Hindawi Publishing Corporation. 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.


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