<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A (di)graph without parallel edges can simply be represented by a binary relation of the vertices and on the other hand, any binary relation can be expressed as such a graph. In this article, this correspondence is formalized in the Mizar system [2], based on the formalization of graphs in [6] and relations in [11], [12]. Notably, a new definition of createGraph will be given, taking only a non empty set <italic>V</italic> and a binary relation <italic>E</italic> ⊆ <italic>V × V</italic> to create a (di)graph without parallel edges, which will provide to be very useful in future articles.</p></abstract>

A (di)graph without parallel edges can simply be represented by a binary relation of the vertices and on the other hand, any binary relation can be expressed as such a graph. In this article, this correspondence is formalized in the Mizar system [2], based on the formalization of graphs in [6] and relations in [11], [12]. Notably, a new definition of createGraph will be given, taking only a non empty set V and a binary relation E ⊆ V × V to create a (di)graph without parallel edges, which will provide to be very useful in future articles.

Unification of Graphs and Relations in Mizar

Formalized Mathematics

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{"article-title":"Unification of Graphs and Relations in Mizar"}

A (di)graph without parallel edges can simply be represented by a binary relation of the vertices and on the other hand, any binary relation can be expressed...

Unification of Graphs and Relations in Mizar

Published Online: Jan 09, 2021

Page range: 173 - 186

Accepted: May 31, 2020

DOI: https://doi.org/10.2478/forma-2020-0015

Keywords
graph theory, binary relation

© 2020 Sebastian Koch, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Unification of Graphs and Relations in Mizar

Published Online: Jan 09, 2021

Page range: 173 - 186

Accepted: May 31, 2020

DOI: https://doi.org/10.2478/forma-2020-0015

Keywordsgraph theory, binary relation

© 2020 Sebastian Koch, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
graph theory, binary relation