Brahmagupta, an Indian mathematician, is credited with developing the 'chakravala' method, an ancient technique for solving indeterminate quadratic equations.

The 'chakravala' method is specifically designed for solving Diophantine equations, which are equations with integer coefficients and integer solutions.

The 'chakravala' method can be applied to find optimal routes for transportation by solving Diophantine equations related to distance, time, and cost.

Srinivasa Ramanujan, an Indian mathematician, made significant contributions to graph theory, including the study of highly composite numbers and partitions.

Ramanujan's work on highly composite numbers has applications in optimizing transportation networks by identifying key nodes and connections that can improve efficiency and reduce congestion.

Transportation network graphs are used to represent the relationship between different modes of transportation, such as roads, railways, airways, and waterways, and the connections between them.

Eulerian graphs are used in transportation to find optimal routes by identifying paths that visit all nodes (cities or locations) exactly once, ensuring efficient movement of goods or people.

Flow network graphs are used to represent the flow of traffic in a transportation network, where nodes represent intersections or junctions, and edges represent roads or paths, with capacities indicating the maximum traffic flow allowed.

Flow network graphs are used in transportation to optimize traffic flow by identifying bottlenecks, analyzing traffic patterns, and implementing strategies to improve the efficiency of the transportation network.

Connectivity graphs are used to represent the connectivity of different regions in a transportation network, where nodes represent regions or cities, and edges represent transportation links, indicating the presence of roads, railways, or airways connecting them.

Connectivity graphs are used in transportation to aid in planning transportation infrastructure by identifying areas with poor connectivity, analyzing the impact of new transportation projects, and ensuring equitable access to transportation services.

Distribution graphs are used to represent the distribution of transportation facilities in a region, where nodes represent transportation facilities (such as bus stops, train stations, or airports), and edges represent the connections between them.

Distribution graphs are used in transportation to aid in planning the location of new transportation facilities by identifying areas with high demand, analyzing the impact of new facilities on the existing network, and ensuring efficient distribution of transportation services.

Flow network graphs are used to represent the movement of goods or people in a transportation network, where nodes represent locations or points of interest, and edges represent transportation routes, with capacities indicating the maximum flow allowed.

Flow network graphs are used in transportation to optimize the flow of goods or people by identifying bottlenecks, analyzing traffic patterns, and implementing strategies to improve the efficiency of the transportation network.