Graph Basic In Data structure
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The document provides an overview of graph concepts including definitions of a graph as a pair of vertices and edges, different types of graphs such as directed/undirected graphs and cyclic/acyclic graphs. It also discusses graph coloring, adjacency matrices/lists for representing graphs, and algorithms for traversing graphs including depth-first search and breadth-first search. Examples are given for each concept to illustrate key differences and properties.
Graph Basic In Data structure
- 2. Contents For Our Presentation... 1. what is Graph,vertices and Edge? 2. kinds of Graph. 3. Graph Coloring. 4. Adjacent Matrix. 5. Adjacent List . 6. Depth First search. 7. Breath First search.
- 3. WHAT IS GRAPH? A graph is a pair of (V.E). where 'V ' is a set of Vertices and 'E' is a set of Edges. Vertices Edge
- 4. kinds of Graph: Undirected Graph: In an undirected graph, the order of the vertices in the pairs in the Edge set doesn't matter Directed Graph: In a directed graph the order of the vertices in the pairs in the edge set matters. Cyclic Graph: A cyclic graph is a directed graph with at least one cycle. A cycle is a path along the directed edges from a vertex to itself. The vertex labeled graph above as several cycles.
- 5. Directed Acyclic Graph(DAG): A Dag is a directed graph without cycles. Proper graph: proper graph is a graph that which has no cycle and not more than one Edge.
- 6. Graph Coloring: Graph coloring is a special case of graph labeling,it is an assignment of labels traditionally called "colors" to elements of a Graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.
- 7. Adjacency Matrix: Adjacency matrix: A two-dimensional matrix, in which the rows represent source vertices and columns represent destination vertices. Data on edges and vertices must be stored externally. Only the cost for one edge can be stored between each pair of vertices. A D E
- 8. Adjacency list: Vertices are stored as records or objects, and every vertex stores a list of adjacent vertices. This data structure allows the storage of additional data on the vertices. Additional data can be stored if edges are also stored as objects, in which case each vertex stores its incident edges and each edge stores its incident vertices. For That Example Adjacency list Will be: A->B->E->F->D A->B->C->D A->C->D
- 9. There are two types of traversal 1. Dfs(Depth first search) 2.Bfs(Breadth first search)
- 10. Depth-first search (DFS) : DFS is an algorithm for traversing or searching tree or graph data structures. One starts at the root(selecting some arbitrary node as the root in the case of a graph) and explores as far as possible along each branch before backtracking. 1 0 6 Output: 1 0 5 2 3
- 11. Breadth-first search: (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the tree rootand explores the neighbor nodes first, before moving to the next level neighbours.Compare BFS with the equivalent, but more memory-efficient Interactive deeping depth and contrast with depth-first search and contrast with depth first search. A B c E F H Queue Status OUTPUT : A B S C G D E F H G S
- 12. Thank you...!!!