Publications de l'Institut Mathématique, Nouvelle Série Vol. 92(106), pp. 35–41 (2012) 

DIGRAPHS ASSOCIATED WITH FINITE RINGSAleksandar T. LipkovskiFaculty of Mathematics, University of Belgrade, Belgrade, SerbiaAbstract: Let $A$ be a finite commutative ring with unity (ring for short). Define a mapping $\varphi:A^2\to A^2$ by $(a,b)\mapsto(a+b,ab)$. One can interpret this mapping as a finite directed graph (digraph) $G=G(A)$ with vertices $A^2$ and arrows defined by $\varphi$. The main idea is to connect ring properties of $A$ to graph properties of $G$. Particularly interesting are rings $A=\mathbb Z/n\mathbb Z$. Their graphs should reflect numbertheoretic properties of integers. The first few graphs $G_n=G(\mathbb Z/n\mathbb Z)$ 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. Keywords: finite rings; finite graphs; symmetric polynomials Classification (MSC2000): 11T99; 05C90 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 8 Nov 2012. This page was last modified: 19 Nov 2012.
© 2012 Mathematical Institute of the Serbian Academy of Science and Arts
