Hamiltonian property of intersection graph of zero divisors of the ring $Z_n$

Shaik Sajana; D Bharathi

doi:10.26637/MJM0601/0017

Abstract

The intersection graph $G_Z^{\prime}\left(Z_n\right)$ of zero-divisors of the ring $Z_n$, the ring of integers modulo $n$ is a simple undirected graph with the vertex set is $Z\left(Z_n\right)^*=Z\left(Z_n\right) \backslash\{0\}$, the set of all nonzero zero-divisors of the ring $Z_n$ and for any two distinct vertices are adjacent if and only if their corresponding principal ideals have a nonzero intersection. We determine some results concerning the necessary and sufficient condition for the graph $G_Z^{\prime}\left(Z_n\right)$ is Hamiltonian. Also, we investigate for all values of for which the graph $G_Z^{\prime}\left(Z_n\right)$ is Hamiltonian and as an example we show that how the results give as easy proof of the existence of a Hamilton cycle.

Keywords:

Finite commutative ring,, Zero-divisors, Principal ideals, Intersection graph, Hamilton Cycle

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Shaik Sajana Department of Mathematics, S.V. University, Tirupati-517502, India.
D Bharathi Department of Mathematics, S.V. University, Tirupati-517502, India.

Pages: 133-139
Date Published: 01-01-2018
Vol. 6 No. 01 (2018): Malaya Journal of Matematik (MJM)

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