Geodesic
Groups and Monoids of Regular Graphs (And of Graphs with Bounded Degrees)
Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 239-251

Voir la notice de l'article provenant de la source Cambridge University Press

A graph X is a set V(X) (the vertices of X) with a system E(X) of 2-element subsets of V(X) (the edges of X). Let X, Y be graphs and f : V(X) → V(Y) a mapping; then/ is called a homomorphism of X into F if [f(x),f(y)] ∈ E(Y) whenever [x,y] ∈ E(X). Endomorphisms, isomorphisms and automorphisms are defined in the usual manner.Much work has been done on the subject of representing groups as groups of automorphisms of graphs (i.e., given a group G, to find a graph X such that the group of automorphisms of X is isomorphic to G). Recently, this was related to category theory, the main question being as to whether every monoid (i.e., semigroup with 1) can be represented as the monoid of endomorphisms of some graph in a given category of graphs. 
Hell, Pavol; Nešetřil, Jaroslav. Groups and Monoids of Regular Graphs (And of Graphs with Bounded Degrees). Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 239-251. doi: 10.4153/CJM-1973-024-8
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[1] 1. Frucht, R., Graphs of degree three with a given abstract group, Can. J. Math. 1 (1949), 365–378. Google Scholar

[2] 2. Hedrlin, Z. and Lambek, J., How comprehensive is the category of semigroups? J. Algebra 11 (1969), 195–212. Google Scholar

[3] 3. Hedrlin, Z. and Mendelsohn, E., The category of graphs with a given subgraph - with applications to topology and algebra, Can. J. Math. 21 (1969), 1506–1517. Google Scholar

[4] 4. Hedrlin, Z. and Pultr, A., Symmetric relations ﹛undirected graphs) with given semigroups, Monatsh.Math. 69 (1965), 318–322. Google Scholar

[5] 5. Hedrlin, Z. and Pultr, A., On rigid undirected graphs, Can. J. Math. 18 (1966), 1237–1242. Google Scholar

[6] 6. Hell, P. and Nešetřil, J., Graphs and k-societies, Can. Math. Bull. 13 (1970), 375–381. Google Scholar

[7] 7. Hell, P., Full embeddings into some categories of graphs, Algebra Universalis 2 (1972), 129–141. Google Scholar

[7] 7. Hell, P., Full embeddings into some categories of graphs (submitted to Algebra Universalis). Google Scholar

[8] 8. Kurosh, A. G., The theory of groups (Chelsea, New York, 1960). Google Scholar

[9] 9. Mendelsohn, E., Šip-products and graphs with given semigroups(to appear). Google Scholar

[10] 10. Sabidussi, G., Graphs with given group and given graph-theoretical properties, Can. J. Math. 9 (1957), 515–525. Google Scholar

[11] 11. Vopnka, P., Hedrlin, Z. and Pultr, A., A rigid relation exists on any set, Comment. Math. Univ. Carolinae 6 (1965), 149–155. Google Scholar

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