Bipolar Turiyam Graph

Background Bipolar turiyam graphs are a type of graph that extends the concept of turiyam graphs by incorporating bipolar characteristics. They are useful in fields like network theory and combinatorial optimization because they can model complex systems with two-way relationships. Method The research focuses on defining the structural properties of bipolar turiyam graphs through a purely theoretical approach and graph-theoretical techniques. Also, we analyse key metrics like degree, and closed neighborhood degree. Results In this article, we have introduced the concept of bipolar turiyam graphs (BTGs) and explored their fundamental properties and parameters. Conclusion This article 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. This foundational understanding paves the way for further research and applications in graph theory, enhancing our ability to analyze complex networks and relationships.