Role of zero-divisor graph in power set ring

Abdul Jamil Nazary ()

International Journal of Innovative Research and Scientific Studies, 2021, vol. 4, issue 3, 181-185

Abstract: The first article about graph theory was written by Leonhard Euler the famous Swiss mathematician which was published in 1736. Primarily, the idea of graph was not important as point of mathematics because it mostly deals with recreational puzzles. But the recent improvement in mathematics specially, its application brought a strong revolution in graph theory. Therefore, this article is written under the title of (Role of Zero-divisor graph in power set ring). This study clarifies the role of the zero-fraction graph in the strength ring and the library research method was used for the collection of information from the past research. This study first introduces the zero-divisor graph set of alternatives in R ring. Then presents the Role of Zero-divisor graph in power set ring. Whereas the vertex is denoted with K1 and the elements of an optional ring which are not zero-divisors they are the vertices without edges of that ring in zero-divisor graph. Next, we will study when a graph is planar in power set ring. The research found out that if the element numbers of set X is less than 4, the graph of zero-divisor graph ring of P X( ) is planar and if the element numbers of set X is greater than or equals to 4, the zero-divisor graph ring is not planar.

Keywords: Set; Graph; Zero-Divisors; Zero-Divisors’ Graph (search for similar items in EconPapers)
Date: 2021
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