On Zero Divisor Graphs

Please enable javascript in your browser.

Fekri Dabanloo, Yousef | 2013

582 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45158 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Hezavehi, Mohammad
Abstract:
We survey the research conducted on zero divisor graphs, with a focus on zero divisor graphs determined by equivalence classes of zero divisors of a commutative ring R. In particular, we consider the problem of classifying star graphs with any finite number of vertices. We study the pathology of a zero divisor graph in terms of cliques, we investigate when the clique and chromatic numbers are equal, and we show that the girth of a Noetherian ring, if finite, is 3. We also introduce a graph for modules that is useful for studying zero divisor graphs of trivial extensions
Keywords:
Zero-Divisor Graph ; Star Graph ; Commutative Ring

No TOC