Hamiltonian property of intersection graph of zero divisors of the ring extbf{$Z_n$}

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Authors :

Shaik Sajana1* and D Bharathi2

Author Address :

1,2Department of Mathematics, S.V. University, Tirupati-517502, India.

*Corresponding author.

Abstract :

The intersection graph $G_{Z}^{’}(Z_{n})$ of zero-divisors of the ring $Z_n$, the ring of integers modulo $n$ is a simple undirected graph with the vertex set is $Z(Z_{n})^{*} = Z(Z_{n})setminus lbrace0 brace$, 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 $G_{Z}^{’}(Z_{n})$ is Hamiltonian. Also, we investigate for all values of for which the graph $G_{Z}^{’}(Z_{n})$ 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.

DOI :

10.26637/MJM0601/0017

Article Info :

Received : September 24, 2017; Accepted : November 30, 2017.

 

 

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