Structure of Zero Divisor Graphs
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George Simonovich
College:
The Dorothy and George Hennings College of Science, Mathematics, and Technology
Major:
Mathematical Sciences
Faculty Research Advisor(s):
Sardar Mohib Ali Khan
Abstract:
Zero divisor graphs were introduced by I. Beck [1] in 1988 to study the combinatorial and structural properties of a commutative ring R. We will consider the ring of integers modulo n, Zn for our study. The graph structure of zero divisor graph up to isomorphism and invariant like diameter, clique, eccentricity, girth and radius has been discussed in recent years [2, 3] for special cases like
Zp^t or Zp^k × Zq^t for k, t = 1, 2, 3. We will extend the study by investigating the structural and combinatorial properties for k, t > 3 and for composite numbers n = pqr where r can be a power of prime or composite number.
Bibliography
[1] Beck, I. Coloring of a commutative ring, J. Algebra, 116 (1988), 208 - 226.
[2] Pi, Seung Jun. The zero-divisor graph of the ring of integers modulo n, Kyung-
pook Mathematical Journal (2019), 591- 601.
[3] Pirzada, S.On the zero divisor graphs of the rings, Afrika Matematika (2020), 727
- 737.