Metric and Upper Dimension of Extended Annihilating-Ideal Graphs.

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 E A G (R) associated to a commutative ring R , denoted by dim M (E A G (R)) , dim + (E A G (R)) and res (E A G (R)) , respectively. Here we prove the finiteness conditions of dim M (E A G (R)) and dim + (E A G (R)). In addition, we characterize dim M (E A G (R)) , dim + (E A G (R)) and res (E A G (R)) for artinian rings and the direct product of rings. [ABSTRACT FROM AUTHOR]