Search games in graphs have attracted significant attention in recent years, and they have applications in securing computer networks against viruses and intruders. Since graph searching is an NP-hard problem, polynomial-time algorithms have been given for solving it on various graph classes. Most of these algorithms concern computing the node search number of a graph, and only few such algorithms are known for computing the mixed, search or edge search numbers of specific graph classes. In this paper we show that the mixed search number of permutation graphs can be computed in linear time, and we describe an algorithm for this purpose. In addition, we give a complete characterization of the edge search number of complete' bipartite graphs.
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