An algebraic framework of weighted directed graphs
type: Item
instance of: scholarly article
title: An algebraic framework of weighted directed graphs
zbMATH Open document ID: 1031.05061
DOI: 10.1155/S0161171203302170
author: Philippe Leroux
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/50562
review text: Summary: We show that an algebraic formulation of weighted directed graphs leads to introducing a \(k\)-vector space equipped with two coproducts \(\Delta\) and \(\widetilde{\Delta}\) verifying the so-called coassociativity breaking equation \((\widetilde{\Delta} \otimes \text{id})\Delta = (\text{id} \otimes \Delta)\widetilde{\Delta}\). 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.
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 2012638
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2012638