Application of Metric Dimensions to Minimize the Installation of Fire Sensors on The Rectorate Building of Pasifik Morotai University

¹ Department of mathematics, Faculty of Science, Universitas Pasifik, Morotai, Indonesia
² Department of Informatics, Faculty of Engineering, Universitas Khairun, Ternate, Indonesia
³ Department of mathematics, Faculty of Science, Universitas Pasifik, Morotai, Indonesia
⁴ Department of mathematics, Faculty of Science, Universitas Pasifik, Morotai, Indonesia

^* Corresponding author: munazat@unkhair.ac.id

Abstract

The metric dimension of the connected graph G for each 𝑣 𝜖 𝑉(𝐺) to the set W is . The set r (ν|W) = (d(ν, w1), d(ν,w2),…d(ν,wk) W is called the resolving set if every vertex u,v in G, if u ≠ ν , then r (u|W) ≠ r (ν|W) . Then the resolving set with the minimum cardinality can be called the minimum resolving set. The cardinality is called the metric dimension of G and is denoted by dim(G). This study aims to study and apply the concept of metric dimensions to minimize the installation of fire sensors in a building and focus on saving procurement costs and monitoring security against fire hazards. The Rectorate Building of the Pasifik Morotai University is under study, which consists of 3 floors with 55 rooms. From the results of the study, it was obtained that the fire sensors needed on the first floor were three, and on the second floor, three. There were three fire sensors on the third floor, so the number of fire sensors that will be installed in the Morotai University Pacific Rectorate Building is nine, regardless of the relationship between the floors.