Paper Info
Title
On some graph problem in the theory of partial algebras - Part I.
Abstract
In the theory of partial algebras we have, in a natural way, the following algebraic problem: When is a unary partial algebra A of type K uniquely determined (up to isomorphism) by its weak subalgebra lattice in the class of all unary partial algebras of type K? Such monounary partial algebras are characterized in Bartol (Comment. Math. Univ. Carolin. 31 (1990) 411). Unfortunately, from Bartol (Comment. Math. Univ. Carolin. 31 (1990) 405) and Pióro (Czechoslovak Math. J. 50 (125) (2000) 295) it follows that for other classes of unary algebras such a full reconstruction, without additional restrictions onto classes, is rather impossible. On the other hand, each unary partial algebra A of type K can be represented by a digraph D(A) obtained from A by omitting names of operations, and by a graph D∗(A) obtained from the first by omitting the orientation of all edges (see Bartol, 1990 and Pióro, 2000). Secondly, Bartol (1990) shows that D∗(A) uniquely determines the weak subalgebra lattice of A. Thirdly, by Pióro (2000), if A is a unary algebra of type K, then D(A) is of type |K|, i.e. at most |K| edges start from each vertex.
Year
DOI
Venue
2004
10.1016/j.disc.2003.12.017
Discrete Mathematics
Keywords
DocType
Volume
05C20,05C90,05C99,08A55,08A60,08A30
Journal
283
Issue
ISSN
Citations 
1
0012-365X
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Konrad Pióro1363.31