Bipolar Turiyam Graph

Background Graph theory is an essential mathematical tool to model complex networks of relations in computer science, operational research, and decision-making. However, classical graphs and other types of graph models are often inadequate in real-life scenarios where one has to deal with vagueness, incomplete information, and concurrent positive and negative influences. Bipolar Turiyam graphs offer a very expressive mathematical framework that can evaluate both positive and negative memberships simultaneously on four different structural dimensions, providing enhanced modeling capacity for these challenges. Method The study focuses on defining the structural properties of bipolar turiyam graphs through a purely theoretical approach and graph-theoretical techniques. We also analyse key metrics such as degree and closed neighborhood degree. Results In this study, we have introduced the concept of bipolar turiyam graphs (BTGs) and explored their fundamental properties and parameters. Conclusion This study has introduced Bipolar Turiyam Graphs (BTGs), detailing their defining characteristics and key parameters. We explored various types of BTGs, established the concept of the Bipolar Turiyam Set (BTS), and examined the significance of Bipolar Relations within these graphs.