Distance spectrum of some zero divisor graphs

Abstract

In the present article, we give the distance spectrum of the zero divisor graphs of the commutative rings $ \mathbb{Z}_{t}[x]/\langle x^{4} \rangle $ ($ t $ is any prime), $ \mathbb{Z}_{t^2}[x] / \langle x^2 \rangle $ ($ t \geq 3 $ is any prime) and $ \mathbb{F}_{t}[u] / \langle u^3 \rangle $ ($ t $ is an odd prime), where $ \mathbb{Z}_{t} $ is an integer modulo ring and $ \mathbb{F}_{t} $ is a field. We calculated the inertia of these zero divisor graphs and established several sharp bounds for the distance energy of these graphs.

Keywords

• zero divisor graphs
• distance energy
• distance spectrum
• commutative rings