Hi Perumalsamy .M

There are too many applications of graph theory in CS to list here. All of these have countless different applications so I will just give some simple examples. This is by no means an exhaustive list of problems either.

• Matching problems which are used in several contexts that require pairing elements with other elements under some criteria. Kidney exchange is one prominent topic at the moment. Dating websites trying to match people based on their preferences could also be one application, although nowadays they are likely using machine learning instead.
• Graph coloring problems that are suitable for scheduling conflicting occurrences or events to avoid overlap, such as exams in a university or coloring different regions in a map that share borders with each other so that every region has a different color than its neighbors.
• Shortest path problems are used in route planning, such as designing least-cost vehicle routes that visit a set of locations or just finding the shortest path between two points in a map. The following used to be an application of the TSP, but perhaps not anymore (at least if I remember correctly): find the shortest tour to drill holes into pre-specified positions in a circuit board (for inserting components to it) that minimizes the distance of moving the drilling head.
• Tree algorithms for computing minimum spanning trees, where each node could represent a major city and the minimum spanning tree will give the shortest distances between the cities as the crow flies. This could be used as a basis to construct a new shortest length underground transportation network between the cities.
• + Countless other problems and applications that are easy to find via google :)

Best regards,

Juho

As continue of Juho Andelmin answer I can identify next areas of applications of graph theory and her components: Natural Language Processing (NLP), routing networks, Big Data and Data Science, Hypergraph semi-supervised learning etc.

Check this older post for some popular topics of research interest in the field of Graph Theory:

https://www.researchgate.net/post/What_are_the_current_areas_of_research_in_Graph_theory