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The Category of Graphs with a Given Subgraph-with Applications to Topology and Algebra

Published online by Cambridge University Press:  20 November 2018

Z. Hedrlín  and
E. Mendelsohn
Z. Hedrlín
Affiliation:
Charles University, Praha, Czechoslovakia
E. Mendelsohn
Affiliation:
Université de Montréal, Montréal, Québec
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By a graph we mean a pair (X, R) where X is a non-void set and R ⊂ X × X. A mapping f: X → Y is called a compatible map (or morphism) from (X, R) into (Y, S) if 2f(R) ⊂ S, where 2f: X2 → Y2 is defined by 2f((x1, x2)) = (f(x1),f(x2)). The set of all compatible maps from (X, R) into itself forms a monoid (semigroup with a unit element) under composition, which is denoted by M(X, R). A graph (X1, R1) is said to be a full subgraph of (X, R) if X1 ⊂ X and R1 = R ∩ (X1 × X1). A graph (X, R) is said to be without loops if (x, x) ∉ R for all x ∈ X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1506 - 1517
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. de Groot, J., Groups represented by homeomorphism groups. I, Math. Ann. 138 (1958), 80–102 Google Scholar
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3. Hedrlin, Z. and Pultr, A., Symmetric relations ﹛undirected graphs) with given semigroups, Monatsh. Math. 69 (1965), 318–324.Google Scholar
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