Application of Centers and Centroid of Graphs in Determining the Strategic Location of Public Facilities Development on Lombok Island

Abstract

Determining a strategic location in a region can be done using the Center and Centroid of a graph. This involves transforming a region's map into a graph form, then identifying the center and centroid of the graph. The determination of the centroid is done by identifying the minimum spanning tree of the graph using Kruskal's and Prim's algorithms. In this study, strategic location determination was carried out to find suitable places for constructing public facilities such as hospitals, schools, and others on Lombok Island. The results showed that Lenek, Pringgasela, and Suralaga Districts are the most strategic areas in Lombok Timur Regency for building public facilities. For other regencies, namely Lombok Tengah, Lombok Barat, Lombok Utara, and the city of Mataram, one strategic location was found in each, specifically in Praya District, Kediri District, Gangga District, and Selaparang District, respectively.