PROPERTIES OF ZERO-DIVISOR GRAPH OF THE RING $\mathbf{F}_{p^l} \times \mathbf{F}_{q^m} \times \mathbf{F}_{r^n}$

Abstract

In this paper, we study some basic properties of the zero-divisor graph of ring $F_{p^l} \times F_{q^m} \times F_{r^n}$, where $F_{p^l}$, $F_{q^m}$ and $F_{r^n}$ are fields of order $p^l$, $q^m$ and $r^n$, respectively, $p, q$ and $r$ are primes (not necessarily distinct) and $l, m, n \geq 1$ are positive numbers. Also, we discuss some topological indices of the graph $\Gamma(F_{p^l} \times F_{q^m} \times F_{r^n})$.