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@article{175211,
        author = {Kirti Kumar Jain and Sarla Raigar},
        title = {Solving Linear Programming Problems Using Graph Theory Approaches},
        journal = {International Journal of Innovative Research in Technology},
        year = {2025},
        volume = {11},
        number = {11},
        pages = {2124-2127},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=175211},
        abstract = {Linear Programming (LP) is a powerful mathematical technique used for optimizing a linear objective function, subject to a set of linear constraints. Traditionally solved using algebraic methods such as the Simplex algorithm or interior-point methods, recent research has explored the application of graph theory to improve computational efficiency and gain intuitive understanding of LP problems. This paper presents a study on how graph-theoretic concepts—such as networks, flows, shortest paths, and dual graphs—can be applied to model and solve linear programming problems. Special attention is given to network flow problems, where LP models naturally translate into graphical representations. The integration of graph algorithms allows for visual analysis and alternative solution strategies, especially in transportation and assignment problems. The study also highlights the advantages and limitations of using graph-based methods in large-scale LP problems.},
        keywords = {Linear Programming, Graph Theory, Network Flow, Optimization, Shortest Path, Transportation Problem, Assignment Problem, Dual Graphs, Simplex Method, Combinatorial Optimization},
        month = {April},
        }