A study on rough co zero divisor graph of a rough semiring

Abstract

In this thesis an approximation space l = (U, R), where U denotes a newlinenonempty finite set of objects and R denotes an arbitrary equivalence relation newlinedefined on U is considered. The Rough Co-zero divisor graph G(Z*(J)) of a newlineRough Semiring (T,and#916;, )on I corresponding to the Rough ideal l is taken for newlinestudy. Let {X1,X2, Xn} be the n equivalence classes induced by R. newlineWithout loss of generality assume that { X1,X2, Xm} be the m equivalence newlineclasses whose cardinality is greater than one and {Xm+1,Xm+2, .+Xn} newlinebe the n-m _ equivalence classes whose cardinality is equal to one. Let newlineB= {{ x1}, {x2}, . . . , {xm}} be the set of pivot elements chosen from the newlineequivalence classes whose cardinality is greater than one. j = {RS(x) | x and#8712; newlinep(B)} is an ideal called the Rough ideal of the Rough semiring (T, and#916;, _). newlineAlso assume that m is the union of none, one or more of the equivalence classes newlinewhose cardinality is equal to one and quotM is the union of one or more of the newlineequivalence classes whose cardinality is equal to one. newline newline newline