1 research outputs found
Wiener index of the Cozero-divisor graph of a finite commutative ring
Let be a ring with unity. The cozero-divisor graph of a ring , denoted
by , is an undirected simple graph whose vertices are the set of
all non-zero and non-unit elements of , and two distinct vertices and
are adjacent if and only if and . In this
article, we extend some of the results of [24] to an arbitrary ring. In this
connection, we derive a closed-form formula of the Wiener index of the
cozero-divisor graph of a finite commutative ring . As applications, we
compute the Wiener index of , when either is the product of
ring of integers modulo or a reduced ring. At the final part of this paper,
we provide a SageMath code to compute the Wiener index of the cozero-divisor
graph of these class of rings including the ring of integers
modulo