The problems of determining the minimum-sized \emph{identifying}, \emph{locating-dominating} and \emph{open locating-dominating codes} of an input graph are special search problems that are challenging from both theoretical and computational viewpoints. In these problems, one selects a dominating set $C$ of a graph $G$ such that the vertices of a chosen subset of $V(G)$ (i.e. either $V(G)\setminus C$ or $V(G)$ itself) are uniquely determined by their neighborhoods in $C$. A typical line of attack for these problems is to determine tight bounds for the minimum codes in various graphs classes. In this work, we present tight lower and upper bounds for all three types of codes for \emph{block graphs} (i.e. diamond-free chordal graphs). Our bounds are in terms of the number of maximal cliques (or \emph{blocks}) of a block graph and the order of the graph. Two of our upper bounds verify conjectures from the literature - with one of them being now proven for block graphs in this article. As for the lower bounds, we prove them to be linear in terms of both the number of blocks and the order of the block graph. We provide examples of families of block graphs whose minimum codes attain these bounds, thus showing each bound to be tight.

翻译：确定输入图的最小规模**识别码**、**定位支配码**和**开定位支配码**是特殊的搜索问题，从理论和计算角度均具有挑战性。在这类问题中，需要选择图$G$的一个支配集$C$，使得$V(G)$的某个子集（即$V(G)\setminus C$或$V(G)$本身）中的顶点能够通过它们在$C$中的邻域唯一确定。解决这些问题的典型方法是确定各类图中最小码的紧界。本文针对**块图**（即无钻石弦图）给出了这三种码的紧下界和上界。我们的边界基于块图的最大团（或**块**）数量以及图的阶数。其中两个上界验证了文献中的猜想——其中一个在本文中已针对块图得到证明。对于下界，我们证明它们关于块数和块图阶数呈线性关系。我们提供了使最小码达到这些边界的块图族实例，从而表明每个边界都是紧的。