On a variation of zero-divisor graphs
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 c...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
2016
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/14921 |
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| Institution: | De La Salle University |
| Language: | English |
| 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). |
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