In this paper we give an account of the different ways to define homomorphisms of graphs. This leads to six classes of endomorphisms for each gt aph. which as sets always form a chain by inclusion. The endomorphism spectrum is defined as a six-tuple containing the cardinalities of these six sets, an
Endomorphisms of undirected modifications of directed graphs
✍ Scribed by Věra Trnková
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 465 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
In this paper, split graphs with a regular endomorphism monoid are characterized explicitly.
It is shown that given a finite or infinite graph H and a subsemigroup B of its endomorphism semigroup End H, there exists a graph G such that (i) H is an induced subgraph of G, (ii) H is stable by every fe End 6. (iii) every f~ End G is uniquely determined by its restriction to H, (iv) the restric
## Abstract Let __f__(__n__) = min{χ(__G__ × __H__) : __G__ and __H__ are __n__‐chromatic digraphs} and __g__(__n__) = min{χ(__G__ × __H__) : __G__ and __H__ are __n__‐chromatic graphs}. We prove that __f__ is bounded if and only if __g__ is bounded. © 2005 Wiley Periodicals, Inc. J Graph Theory