EULERIAN OF THE ZERO DIVISOR GRAPH $\Gamma[\mathbb {Z}_n]$

Print ISSN: 0972-7752 | Online ISSN: 2582-0850

Abstract

The Zero divisor Graph of a commutative ring $R$, denoted by $\Gamma[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. We consider the zero divisor graph $\Gamma[\mathbb{Z}_n]$, for any natural number $n$ and find out which graphs are Eulerian graphs.

Keywords and Phrases

Zero divisor graph, Euler tour, Euler graph.

A.M.S. subject classification

05C12, 05C25, 05C50.

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