diff --git a/src/main/java/com/thealgorithms/datastructures/graphs/README.md b/src/main/java/com/thealgorithms/datastructures/graphs/README.md index 057adb46acf5..4798e372667b 100644 --- a/src/main/java/com/thealgorithms/datastructures/graphs/README.md +++ b/src/main/java/com/thealgorithms/datastructures/graphs/README.md @@ -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 3 1 0 0 0 1 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)