Graded Hyperideals-Based Graphs on ‎W‎eak Graded Multiplicative Hyperrings

Abstract ‎In this paper‎, ‎we introduce the notion of weak monoid-graded multiplicative hyperrings and present their properties‎, ‎special the relation to monoid-graded multiplicative hyperrings‎. ‎We bring forward the concept of an intersection graph of graded hyperideals of monoid-graded multiplicative hyperrings‎. ‎Indeed‎, ‎for any given monoid and multiplicative hyperring‎, ‎it is introduced the notion of weak monoid-graded multiplicative hyperring‎, ‎so concerning any non avoided subset of given multiplicative hyperring‎, ‎we established special nontrivial graded hyperideals as the vertices and any two vertices are adjacent if have a nonzero intersection‎. ‎We proved that the graded hyperideals of this class of weak monoid-graded multiplicative hyperring are cyclic and computed the set of all graded hyperideals of any finite weak monoid-graded multiplicative hyperrings‎. ‎For any given natural number‎, ‎based on the fundamental theorem of arithmetic‎, ‎and any given prime‎, ‎we characterize the intersection graph of graded hyperideals of finite monoid-graded multiplicative hyperrings‎. MSC(2010): Primary: 05C25; Secondary: 20N20, 16W50.