ABSTRACT. Edge e-dominates an edge if with is the subgraph induced . A set is an edge-edge domination set notated by EED-set if every edge in is e-dominated by an edge in . The edge-edge domination number notated by is the cardinality of a minimum EED-set. A set is a strong edge-edge domination set notated by SEED-set if every edge in is e-dominated strongly by an edge in with the condition and . Strong edge-edge domination number notated by . A set is a weak edge-edge domination set notated by WEED-set if every edge in is e-dominated weakly by an edge in with the condition and . Weak edge-edge domination number notated by . This final project we study about strong edge-edge domination set, weak edge-edge domination set and application edge-edge domination set namely determining the optimal number of security personnel that will be used to secure an area.