Architecting Resilient Communal Habitats: A Treatise on the Application of WheelGraphs to Security Optimization with Codes

Abstract

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 Υ−labelling of class (σ, φ, ψ). An algorithm is established which
will lead to the real life security of housing society.