The zero-divisor Cayley graph of the residue class ring $\left(Z_n, \oplus, \odot\right)$

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DOI:

https://doi.org/10.26637/MJM0703/0036

Abstract

In this paper the notion of the zero-divisor Cayley graph $G\left(Z_n, D_0\right)$, where $\left(Z_n, \oplus, \odot\right)$ is the ring of residue classes modulo $n, n \geq 1$, an integer and $D_0$ is the set of nonzero zero-divisors, is introduced and it is shown that $G\left(Z_n, D_0\right)$ can be decomposed into components, if $n$ is a power of a single prime and it is connected, if $n$ is a product of more than one prime power.

Keywords:

Zero-Divisors, Symmetric set, Cayley Graph, Zero-divisor Cayley Graph

Mathematics Subject Classification:

Mathematics
  • Jangiti Devendra Department of Applied Mathematics, Yogi Vemana University, Kadapa-516003, Andhra Pradesh, India.
  • Levaku Madhavi Department of Applied Mathematics, Yogi Vemana University, Kadapa-516003, Andhra Pradesh, India.
  • Tippaluri Nagalakshumma Department of Applied Mathematics, Yogi Vemana University, Kadapa-516003, Andhra Pradesh, India.
  • Pages: 590-594
  • Date Published: 01-07-2019
  • Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)

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Published

01-07-2019

How to Cite

Jangiti Devendra, Levaku Madhavi, and Tippaluri Nagalakshumma. “The Zero-Divisor Cayley Graph of the Residue Class Ring $\left(Z_n, \oplus, \odot\right)$”. Malaya Journal of Matematik, vol. 7, no. 03, July 2019, pp. 590-4, doi:10.26637/MJM0703/0036.

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Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)

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