Graphs of morphisms of graphs

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

Fersiynau electronig

  • Ronald Brown
  • Ifor Morris
  • John Shrimpton
  • Christopher D. Wensley
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 We extend Shrimpton's (unpublished) investigations on the morphism digraphs of reflexive digraphs to the undirected case by using an equivalence between a category of reflexive, undirected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.

Allweddeiriau

Iaith wreiddiolSaesneg
Rhif yr erthyglA1
Nifer y tudalennau28
CyfnodolynThe Electronic Journal of Combinatorics
Cyfrol15
Rhif y cyfnodolyn1
StatwsCyhoeddwyd - 2008
Gweld graff cysylltiadau