EULERIAN OF THE ZERO DIVISOR GRAPH $\Gamma[\mathbb {Z}_n]$
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 121
DOI:
Author :
B. Surendranath Reddy (Department of Mathematics, Swami Ramanand Teerth Marathwada University, Nanded - 431606, Maharashtra, INDIA)
Rupali S. Jain (Department of Mathematics, Swami Ramanand Teerth Marathwada University, Nanded - 431606, Maharashtra, INDIA)
N. Laxmikanth (Department of Mathematics, Swami Ramanand Teerth Marathwada University, Nanded - 431606, Maharashtra, INDIA)
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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