Multidisciplinary Approaches to Strengthening Residential Security Using Graph Theory

Abstract

Security of people is always a big issue in any housing project. Many smart solutions have been discovered regarding this. In this research, we have developed some models regarding security of housing societies. Graph theory plays a vital role in every problem of life. Planar graphs in graph theory are the graphs where no edges cross each other. These graphs are very helpful in making security structures of housing projects where all the vertices (houses) are connected to one another. The models in this study will be very good at optimizing cost and will be user friendly. Secure housing is a fundamental pillar of stable and thriving communities. It encompasses the provision of safe and reliable shelter, where individuals and families can live without fear of harm, theft, or intrusion. Security plan of a housing society can be constructed in many ways. In this article, authors have discovered a plan to strengthen security of a housing society by using face irregularity strength on wheel graphs which contains vertices, edges and faces. The vertices will act like houses, edges will be connections between houses and faces will represent the area among the houses. Mathematically, this research includes irregularity strength of face, vertex-face, edge-face and vertex-edge-face under labelling of class . An algorithm is established which will lead to the real life security of housing society.