Domination Number of the Rough Zero Divisor Graph of the Rough Semiring

Abstract

In this paper, we consider an approximation space I = (U,R).where U is non
empty finite set and R is an arbitrary equivalence relation on U. We define the dominating
set of the Rough zero divisor graph G(Z T
∗
) of the Rough Semiring T, where Z T
∗

denotes the set of nonzero zero divisor of T. We construct a minimal dominating set on T.
We also prove that the domination number of G(Z T
∗
) is equal to the number of
equivalence classes induced by R on U. We illustrate these concepts with suitable examples.