Graph searching is one of the simplest and most widely used tools in graph algorithms. Every graph search method is defined using some particular selection rule, and the analysis of the corresponding vertex orderings can aid greatly in devising algorithms, writing proofs of correctness, or recognition of various graph families. We study graphs where the sets of vertex orderings produced by two different search methods coincide. We characterise such graph families for ten pairs from the best-known set of graph searches: Breadth First Search (BFS), Depth First Search (DFS), Lexicographic Breadth First Search (LexBFS) and Lexicographic Depth First Search (LexDFS), and Maximal Neighborhood Search (MNS).

翻译：图表搜索是图表算法中最简单和最广泛使用的工具之一。 每个图表搜索方法都是使用某种特定的选择规则来定义的,对相应的顶点订单的分析可以极大地帮助设计算法、正确性的书面证明或对不同图形家族的识别。 我们研究由两种不同搜索方法产生的顶点订单组合相交的图表。 我们从最著名的图表搜索组中为十对图形家族定性为十对:Breadth First Search(BFS)、Bload First Search(DFS)、LexBFS、LexBFS 和Lexiclogiclogic 深度第一次搜索(LexDFS)和MMS Maximal Neghborous搜索(MNS)。