A set D of vertices in a graph G is a locating-dominating set if for every two vertices u, v of \(V-D\) the sets \(N_{G}(u)\cap D\) and \(N_{G}(v)\cap D\) are non-empty and different. The locating-domination number \(\gamma _{L}(G)\) is the minimum cardinality of a locating-dominating set of G. A graph G is \(\gamma _{L}\)-dot-critical if contracting any edge of G decreases its locating-domination number. Let \(k\ge 3\) be an integer. A graph G is called k-\(\gamma _{L}\)-dot-critical if G is \(\gamma _{L}\)-dot-critical with \(\gamma _{L}\left( G\right) =k.\) In this paper, we characterize all connected 3-\(\gamma _{L}\)-dot-critical graphs.

一组d中的曲线的顶点的ģ为定位支配集如果对于每两个顶点ü，  v的\（VD \）集合\（N_ {G}（U）\帽d \）和\（N_ { G}（v）\ cap D \）是非空且不同的。定位-控制数\（\伽马_ {L}（G）\）是定位支配集的最小基数ģ。如果收缩G的任意一条边会减少其定位支配数，则图G是\（\ gamma _ {L} \） -点关键的。令\（k \ ge 3 \）为整数。图G称为k- \（\ gamma _ {L} \） -如果G为\（\ gamma _ {L} \） -点临界-具有\（\ gamma _ {L} \ left（G \ right）= k的点临界。\）在本文中，我们描述了所有连通的3- \（\ gamma _ {L} \） -点临界图。