• M.Durgadevi
• G. Bhavana Priya
• S.Naga durga

In mathematics, graph proposition is the study of graphs, which are fine structures used to model brace wise relations between objects. A graph in this environment is made up of vertices (also called bumps or points) which are connected by edges (also called links or lines). Graphs can be used to model numerous types of relations and processes in physical, natural, social and information systems. Numerous practical problems can be represented by graphs. Emphasizing their operation to real- world systems, the term network is occasionally defined to mean a graph in which attributes are associated with the vertices and edges, and the subject that expresses and understands the real- world systems as a network is called network wisdom. Linear programming is an important subject. Linear programming is used for carrying the most optimal result for a problem with given constraints. In direct programming, we formulate our real- life problem into a fine model. It involves an objective function, direct inequalities with subject to constraints. When you have a problem that involves a variety of resource constraints, direct programming can induce the stylish possible result. Whether it's maximizing effects like profit or space, or minimizing factors like cost and waste, using this tool is a quick and effective way to structure the problem, and find a result.

Graph theory, linear programming, Real world systems, Networks, Maximizing and Minimizing.

"Graph theory In Linear programming", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.9, Issue 3, page no.d468-d481, March-2022, Available :http://www.jetir.org/papers/JETIR2203360.pdf

"Graph theory In Linear programming", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.9, Issue 3, page no. ppd468-d481, March-2022, Available at : http://www.jetir.org/papers/JETIR2203360.pdf