Construction of Zero Divisor Graphs of Rings

D. Baruah

doi:https://doi.org/10.14445/22315373/IJMTT-V48P525

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 48 | Number 3 | Year 2017 | Article Id. IJMTT-V48P525 | DOI : https://doi.org/10.14445/22315373/IJMTT-V48P525

Construction of Zero Divisor Graphs of Rings

D. Baruah

Abstract

If R is a commutative ring, 𝑍(𝑅) is the set of zero-divisor of 𝑅 and 𝑍 ∗ (𝑅) = 𝑍(𝑅) − {0}, then the zero-divisor graph of R, Γ (Z*(𝑅)) usually written as 𝛤(𝑅), is the graph in which each element of Z*(𝑅) is a vertex and two distinct vertices x and y are adjacent if and only if 𝑥𝑦 = 0. In this paper we present a construction of zero divisor graphs of rings. In particular we consider ring of Gaussian integers modulo n, i.e. 𝛤 ℤ𝑛 [𝑖].

Keywords

Bipartite graph, Complete bipartite graph, Girth of a graph, Ring of Gaussian integers modulo n, Zero-divisor.

References

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Citation :

D. Baruah, "Construction of Zero Divisor Graphs of Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 48, no. 3, pp. 180-185, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V48P525