Abstract
Monochromatic and rainbow connectivity are known as the concepts that can calculate the minimum number of passwords and security systems. In this paper, a security system is represented by a special mathematics object, namely a graph. The study focuses on the moon graphs or Mon. Moon graphs are chosen because it is one of the 4-connected graphs that has a minimum number of edges. The research method used is mathematical modeling equipped with direct proves and contradictions. The conclusion is that there is an efficiency of 75% when using the monochromatic connected number, and there is an efficiency between 62.5% - 75% when using the rainbow 4-connected number.
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