Metric and Upper Dimension of Extended Annihilating-Ideal Graphs  

作　　者：S.Nithya G.Elavarasi Genghua Fan 

机构地区：[1]Department of Mathematics,St.Xavier's College(Autonomous)Palayamkottai 627002,Tamil Nadu,India [2]Afiliated to Manonmaniam Sundaranar University Abishekapatti,Tirunelveli 627012,Tamil Nadu,India [3]PG and Research Department of Mathematics,St.Xavier's College(Autonomous)Palayamkottai 627002,Tamil Nadu,India [4]Affiliated to Manonmaniam Sundaranar University Abishekapatti,Tirunelveli 627012,Tamil Nadu,India [5]不详

出　　处：《Algebra Colloquium》2024年第2期221-238,共18页代数集刊（英文版）

摘　　要：The metric dimension problem is called navigation problem due to its application to robot navigation in space.Further this concept has wide applications in motion planning,sonar and loran station,and so on.In this paper,we study certain results on the metric dimension,upper dimension and resolving number of extended annihilating-ideal graph EAG(R)associated to a commutative ring R,denoted by dim M(EAG(R)),dim+(EAG(R))and res(EAG(R)),respectively.Here we prove the finiteness conditions of dim M(EAG(R))and dim+(EAG(R)).In addition,we characterize dim M(EAG(R)),dim+(EAG(R))and res(EAG(R))for artinian rings and the direct product of rings.

关 键 词：extended annihilating-ideal graph metric dimension upper dimension resolving number 

分 类 号：O15[理学—数学]