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Update README.md and add some description (#5886)

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Ayush Majumder
2024-10-27 00:25:41 +05:30
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@ -88,4 +88,39 @@ It means there are edges from 0 to 1, 2, and 3; from 1 to 0 and 2, and so on.
2 1 1 0 0 0 2 1 1 0 0 0
3 1 0 0 0 1 3 1 0 0 0 1
4 0 0 0 1 0 4 0 0 0 1 0
```
###Graph Terminologies
Degree of a vertex: Number of edges that are incident at a vertex.
Weighted graph: A graph that has weights assigned for each of the edges (used in cases such as shortest path problems).
Connected components: A set of vertices that can reach others from it but not to those outside this connected component.
Cycle: A path that begins and ends at the same vertex.
Bipartite Graph: A graph whose vertices can be partitioned into two disjoint sets, with every edge connecting a vertex in one set to a vertex in the other set.
###Graph Algorithms
Breadth-First Search: It explores neighbors in layer after layer and applies on shortest path problems for unweighted graphs.
Depth-First Search (DFS): It continues moving up as far along each branch as possible before backtracking. DFS is typically used for traversing all nodes and testing connectivity.
Dijkstra's Algorithm: This algorithm finds the shortest path from a single starting vertex to all other vertices in a weighted graph.
Prim's and Kruskal's Algorithm: To find the minimum spanning tree.
Bellman-Ford Algorithm: This algorithm solves shortest path problems even when there are negative weights.
Graph Types
Multigraphs: Graphs with more edges between the same set of vertices.
Complete Graphs: A graph in which there is a unique edge between each pair of vertices.
Planar Graphs: A graph that can be drawn in a plane such that no two edges cross.
###Graph Algorithm Applications
Google Maps (Dijkstra's Algorithm): How maps apps find shortest routes.
Job Scheduling: Topological Sort A real application of DAG (Directed Acyclic Graph) to manage the dependency of jobs between tasks.
Web Crawling: How to use BFS for web crawlers to index pages in search engines.
Big-O Complexity of Graph Operations
Adjacency List vs Adjacency Matrix : Provide comparison tables of time complexity for operations such as addition of an edge, checking if an edge exists, etc.
BFS and DFS Complexity : Describe their computational cost
###Common Graph Problems
Graph Coloring
Finding Bridges and Articulation Points
Finding Strongly Connected Components
Maximum Flow (Ford-Fulkerson algorithm)