Digraphs associated with finite rings
| Autor: | Aleksandar Lipkovski |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Ring (mathematics) General Mathematics 010102 general mathematics Digraph 0102 computer and information sciences Directed graph Commutative ring 01 natural sciences Combinatorics Symmetric polynomial 010201 computation theory & mathematics 0101 mathematics Graph property Mathematics |
| Zdroj: | Publications de l'Institut Math?matique (Belgrade). 92:35-41 |
| ISSN: | 1820-7405 0350-1302 |
| DOI: | 10.2298/pim1206035l |
| Popis: | Let A be a finite commutative ring with unity (ring for short). Define a mapping ? : A2 ? A2 by (a, b) 7? (a + b, ab). One can interpret this mapping as a finite directed graph (digraph) G = G(A) with vertices A2 and arrows defined by ?. The main idea is to connect ring properties of A to graph properties of G. Particularly interesting are rings A = Z/nZ. Their graphs should reflect number-theoretic properties of integers. The first few graphs Gn = G(Z/nZ) are drawn and their numerical parameters calculated. From this list, some interesting properties concerning degrees of vertices and presence of loops are noticed and proved. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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