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Graphs of morphisms of graphs

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Graphs of morphisms of graphs. / Brown, Ronald; Morris, Ifor; Shrimpton, John et al.
In: The Electronic Journal of Combinatorics, Vol. 15, No. 1, A1, 2008.

Research output: Contribution to journal › Article › peer-review

HarvardHarvard

Brown, R, Morris, I, Shrimpton, J & Wensley, CD 2008, 'Graphs of morphisms of graphs', The Electronic Journal of Combinatorics, vol. 15, no. 1, A1. <https://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1a1/pdf>

APA

Brown, R., Morris, I., Shrimpton, J., & Wensley, C. D. (2008). Graphs of morphisms of graphs. The Electronic Journal of Combinatorics, 15(1), Article A1. https://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1a1/pdf

CBE

Brown R, Morris I, Shrimpton J, Wensley CD. 2008. Graphs of morphisms of graphs. The Electronic Journal of Combinatorics. 15(1):Article A1.

MLA

Brown, Ronald et al. "Graphs of morphisms of graphs". The Electronic Journal of Combinatorics. 2008. 15(1).

VancouverVancouver

Brown R, Morris I, Shrimpton J, Wensley CD. Graphs of morphisms of graphs. The Electronic Journal of Combinatorics. 2008;15(1):A1.

Author

Brown, Ronald ; Morris, Ifor ; Shrimpton, John et al. / Graphs of morphisms of graphs. In: The Electronic Journal of Combinatorics. 2008 ; Vol. 15, No. 1.

RIS

TY - JOUR

T1 - Graphs of morphisms of graphs

AU - Brown, Ronald

AU - Morris, Ifor

AU - Shrimpton, John

AU - Wensley, Christopher D.

PY - 2008

Y1 - 2008

N2 - 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 We extend Shrimpton's (unpublished) investigations on the morphism digraphs of reflexive digraphs to the undirected case by using an equivalence between a category of reflexive, undirected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.

AB - 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.

KW - graph, digraph, cartesian closed category, tops, endomorphism mooned, symmetry object

M3 - Article

VL - 15

JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

IS - 1

M1 - A1

ER -