In this presentation, titled “Graph Theory and Applications”, we will go through a comprehensive exploration of graph theory, covering fundamental concepts, real-world applications, and intriguing connections to both nature, gaming and the computer world. The audience will delve into the basics of graph theory, understand graphs as mathematical structures comprising nodes and edges with various types and essential terminology. The presentation introduces a fascinating behavior of slime mold, inspiring bio-inspired algorithms for optimization problems. Transitioning to computer science, the session showcase how graphs model relationships in computer networks, and social networks, followed by insights into critical graph algorithms like Breadth-First Search, Dijkstra’s Algorithm, and A* Algorithm, emphasizing their applications in navigation and route planning. Also, a connection is drawn between graph theory and the strategic game of Sprouts, revealing how graph structures underpin the game’s dynamics and strategy. Real-world applications in emerging trends such as blockchain, cybersecurity, biology, and machine learning were highlighted, showcasing the practical relevance of graph theory. The presentation will conclude with a glimpse into future research areas, particularly in quantum walks.