A set W ⊆ V (G) is called a resolving set, if for each pair of distinct verticesis the distance between vertices x and y. The cardinality of a minimum resolving set for G is called the metric dimension of G and is denoted by dim M (G). This parameter has many applications in different areas. The problem of finding metric dimension is NPcomplete for general graphs but it is determined for trees and some other important families of graphs. In this paper, we determine the exact value of the metric dimension of Andrásf ai graphs, their complements and And(k) P n . Also, we provide upper and lower bounds for dim M (And(k) C n ).

Let R be a commutative ring and M be a Noetherian R-module. The intersection graph of annihilator submodules of M , denoted by GA(M) is an undirected simple graph whose vertices are the classes of elements of ZR(M) \ AnnR(M), for a, b ∈ R two distinct classes [a] and [b] are adjacent if and only if AnnM (a) ∩ AnnM (b) = 0. In this paper, we study diameter and girth of GA(M) and characterize all modules that the intersection graph of annihilator submodules are connected. We prove that GA(M) is complete if and only if ZR(M) is an ideal of R. Also, we show that if M is a finitely generated R-module with r(AnnR(M)) = AnnR(M) and |m − AssR(M)| = 1 and GA(M) is a star graph, then r(AnnR(M)) is not a prime ideal of R and |V (GA(M))| = | Min AssR(M)| + 1.

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