For a connected graph G(V, E), a vertex \(w\in V(G)\) strongly resolves two vertices \(u, v \in V(G)\) if there exists a shortest \(u-w\) path containing v or a shortest \(v-w\) path containing u. A set S of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong resolving set for G is called the strong metric dimension of G. Let R be a commutative ring with identity, and let Z(R) be the set of zero-divisors of R. The annihilator graph of R is a simple graph with the vertex set \(Z(R)^*=Z(R){\setminus }\{0\}\), and two distinct vertices x and y are adjacent if and only if \(ann_R(xy)\ne ann_R(x)\cup ann_R(y)\). In this paper, we study the strong metric dimension of annihilator graphs associated with commutative rings and some strong metric dimension formulae for annihilator graphs are given.

对于连通图G（V，  E），如果存在最短的\（uw \），则顶点\（w（in V（G）\）强烈解析两个顶点\（u，v \ in V（G）\））包含v的路径或包含u的最短\（vw \）路径。一套小号顶点的是一个强大的解决一套摹如果每对顶点摹是强烈的一些顶点解决小号。一个强大的解决集的最小基数ģ被称为的强度量维度ģ。让R是具有同一性的交换环，和让Ž（[R ）是集合的零除数ř。R的an灭子图是具有顶点集\（Z（R）^ * = Z（R）{\ setminus} \ {0 \} \）的简单图，并且当且仅当两个不同的顶点x和y相邻如果\（ann_R（xy）\ ne ann_R（x）\ cup ann_R（y）\）。本文研究了与交换环相关联的an灭子图的强度量维，并给出了dimension灭子图的一些强度量维公式。