Exploring Graph Theory For Practical Solutions

SAVITA S SHINDE; VIJAY. M.P; SHIVAKUMAR MD

doi:10.36676/irt.v4.i8.1556

Authors

SAVITA S SHINDE Lecturer, Dept of Science , Govt Polytechnic – Belagavi,
VIJAY. M.P Lecturer , Dept of Science, Govt Polytechnic-Chamarajanagar
SHIVAKUMAR MD Lecturer , Dept of Science, Govt Polytechnic-Chamarajanagar

DOI:

https://doi.org/10.36676/irt.v4.i8.1556

Keywords:

Eulerian graph, Hamiltonian graphs and cycles, Chromatic number, Tree, Kuratowski’s theorem, Dijkstra’s algorithm.

Abstract

Graph theory is widely used to prove many mathematical theorems and models. This paper present the various applications and techniques of graph theory to solve problems in different fields of science and technology in addition to mathematics. A graph can be used to represent almost any physical situation involving discrete objects and a relationship among them. This abstract provides a concise overview of graph theory’s foundational principles, including graph types(such as directed, undirected, weighted, and unweighted graphs), basics terminologies( vertices, edges, paths, cycles), and essential theorems (e.g, Euler’s theorem Hamiltonian cycles). Moreover, it highlights practical applications of graph theory, such as shortest path algorithms (e.g., Dijkstra’s algorithm), network flow optimization, and graph coloring problems. By unraveling the intricacies of graph theory, this abstract aims to foster a deeper understanding of its role in shaping modern computational paradigms and problem-solving methodologies. These fields include website design, chemistry, biology, computer science, software engineering & operations research.

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