#### Title

On a variation of zero-divisor graphs

#### Date of Publication

2016

#### Document Type

Bachelor's Thesis

#### Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

#### Subject Categories

Mathematics

#### College

College of Science

#### Department/Unit

Mathematics and Statistics Department

#### Thesis Adviser

Leonor Ruivivar

#### Abstract/Summary

In this study, we define a variation of the zero divisor graph by considering a ring R with unity which is not necessarily commutative. Let {u100000}1(R) be a graph whose vertex set is the set of all nonzero elements of R. If x y 2 V ({u100000}1(R)), then x is adjacent to y if one of the following conditions holds: (a) xy = 0, (b) yx = 0 or (c) x + y is a unit in R. This study has a two main objectives. First, it gives an exposition of Gupta, Sen and Ghosh's A Variation of Zero-Divisor Graphs. The paper determines conditions under which the graph {u100000}1(R) is connected, and when {u100000}1(R) will be isomorphic to some common classes of graphs. If F is a nite eld, the graph theoretic properties of {u100000}1(F) will also be investigated. Second, based on the results presented in the paper, the researchers present some new results on a number of graph theoretic invariants of {u100000}1(R).

#### Abstract Format

html

#### Language

English

#### Format

Electronic

#### Accession Number

CDTU020959

#### Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

#### Physical Description

1 computer disc ; 4 3/4 in.

#### Keywords

Commutative rings

#### Recommended Citation

Asio, Y. Q., & Antiquiera, E. D. (2016). On a variation of zero-divisor graphs. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/14921

#### Embargo Period

5-11-2021