An algebraic framework of weighted directed graphs

IF 1 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-03-15 DOI:10.1155/S0161171203302170

P. Leroux

引用次数: 24

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.

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加权有向图的代数框架

我们证明了加权有向图的代数公式导致引入一个具有两个协积Δ和Δ ~的k向量空间，验证了所谓的协结合性破缺方程(Δ ~⊗id)Δ=(id⊗Δ)Δ ~。这样的空间叫做l -协代数。构造了这种空间的显式示例，并给出了图论与协协代数之间的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Mathematics-Mathematics (miscellaneous)

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

17 weeks

期刊介绍： The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.