A note on simple graphic algebras

✍ Scribed by Juhani Nieminen

• Publisher: John Wiley and Sons
• Year: 1975
• Tongue: English
• Weight: 223 KB
• Volume: 21
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19750210147

✦ Synopsis

A NOTE ON SIMPLE GRAPHIC ALGEBRAS by JUHANT NIEMTNEN in Helsinki (Finland) 111 troduction Several authors have studied the structure of algebras with a ternary operation called median operation, scc e.g. [I], [2], [3], [4], and [7]. Most of the authors have concentrated on the lattice and tree structures while I,. NEBESKG has extended the study t o contain a class of undirected, finite graphs [ 5 ] , [6]. I n this note we shall formulate Home conditions giving a criterion for a class of graphs, called by L. NEBESKG median graphs.

1. Some basic concepts and notations

I n this note we shall use thc concepts defined by L. NEBESKY in [ 5 ] . An ordered pair ( V , &) is a graphic algebra, if V is a non-empty set and Q a closed ternary operation on V such that for every a, b, c E V