Graphs of morphisms of graphs
type: Item
instance of: scholarly article
title: Graphs of morphisms of graphs
zbMATH Open document ID: 1187.18002
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/117194
full work available at URL: v15i1a1.html
review text: Summary: This is an account for the combinatorially minded reader of various categories of directed and undirected graphs, and their analogies with the category of sets. As an application, the endomorphisms of a graph are in this context not only composable, giving a monoid structure, but also have a notion of adjacency, so that the set of endomorphisms is both a monoid and a graph. We extend Shrimpton's (unpublished) investigations on the morphism digraphs of reflexive digraphs to the undirected case by using an equivalence between a category of reflexive, undirected graphs and the category of reflexive, directed graphs with reversal. In so doing, we emphasise a picture of the elements of an undirected graph, as involving two types of edges with a single vertex, namely `bands' and `loops'. Such edges are distinguished by the behaviour of morphisms with respect to these elements.
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18D15
zbMATH DE Number: 5540862
zbMATH Keywords: graph
zbMATH Keywords: digraph
zbMATH Keywords: Cartesian closed category
zbMATH Keywords: topos
author: Ronald Brown
author: I. Morris
author: J. Shrimpton
author: C. D. Wensley
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5540862