Abstract : Graph searching involves a team of mobile agents (called searchers or pursuers or cops) that aims at cap- turing a set of escaping agents (called evaders or fugitives or robbers) that hide in a network modeled by a graph. There are many variants of graph searching studied in the literature, often referred to as a pursuit- evasion game or cops and robbers game. These variants are either application driven, i.e. motivated by problems in practice, or are inspired by foundational issues in Computer Science, Discrete Mathematics, and Artificial Intelligence. Thus many researchers from different areas of Mathematics, Computer Science and Operations Research are interested in quite similar problems around graph searching.