Comaximal factorization graphs in integral

Shafiq Ur Rehman
Department of Mathematics, COMSATS Institute of Information Technology, Attock,
Pakistan.

\(^{1}\)Corresponding Author: shafiq@ciit-attock.edu.pk

Copyright © 2013 Shafiq Ur Rehman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2013.

Abstract

In [1], I. Beck introduced the idea of a zero divisor graph of a commutative ring and later in [2], J. Coykendall and J. Maney generalized this idea to study factorization in integral domains. They defined irreducible divisor graphs and used these irreducible divisor graphs to characterize UFDs. We define comaximal factorization graphs and use these graphs to characterize UCFDs defined in [3]. We also study that, in certain cases, comaximal factorization graph is formed by joining r copies of thecomplete graph \(K_m\) with one copy of complete graph \(K_n\) in common.

Keywords:

Factorization, integral domain, complete graph, windmill graph.