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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oai:animorepository.dlsu.edu.ph:etd_bachelors-62552021-05-12T02:48:52Z On a variation of zero-divisor graphs Asio, Ysac Jericho Q. Antiquiera, Eleonor D. 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). 2016-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/14921 Bachelor's Theses English Animo Repository Commutative rings Mathematics |
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Commutative rings Mathematics |
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Commutative rings Mathematics Asio, Ysac Jericho Q. Antiquiera, Eleonor D. On a variation of zero-divisor graphs |
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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). |
| format |
text |
| author |
Asio, Ysac Jericho Q. Antiquiera, Eleonor D. |
| author_facet |
Asio, Ysac Jericho Q. Antiquiera, Eleonor D. |
| author_sort |
Asio, Ysac Jericho Q. |
| title |
On a variation of zero-divisor graphs |
| title_short |
On a variation of zero-divisor graphs |
| title_full |
On a variation of zero-divisor graphs |
| title_fullStr |
On a variation of zero-divisor graphs |
| title_full_unstemmed |
On a variation of zero-divisor graphs |
| title_sort |
on a variation of zero-divisor graphs |
| publisher |
Animo Repository |
| publishDate |
2016 |
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https://animorepository.dlsu.edu.ph/etd_bachelors/14921 |
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1772834696343846912 |