arXiv subjects

Rupali. S. Jain

Publications and source records attributed to Rupali. S. Jain.

2 recordsLinked to original sources

arXiv2018

Vertex and Edge connectivity of the zero divisor graph $Γ[\mathbb {Z}_n]$

The Zero divisor Graph of a commutative ring $R$, denoted by $Γ[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. In this paper we derive the Vertex and Edge Connectivity of the zero divisor graph $Γ[\mathbb{Z}_n]$, for any natural number $n$ . We also discuss the minimum degree of the zero divisor graph $Γ[\mathbb{Z}_n]$.

math.RA↗

arXiv2017

Eigenvalues and Wiener index of the Zero Divisor graph $Γ[\mathbb {Z}_n]$

The Zero divisor Graph of a commutative ring $R$, denoted by $Γ[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. In this paper, we consider the zero divisor graph $Γ[\mathbb{Z}_n]$ for $n=p^3$ and $n=p^2q$ with $p$ and $q$ primes. We discuss the adjacency matrix and eigenvalues of the zero divisor graph $Γ[\mathbb{Z}_n]$. We also calculate the energy of the graph $Γ[\mathbb{Z}_n]$.

math.RA↗