A graph G consists of two sets:

(i) A set V, Called the set of all vertices( or nodes)

(ii) A str V, called the set of all edges. This set E is the set of all pairs of elements from V.

**1. Directed Graph:** A digraph is also called a directed graph. It is a graph G, where each edge have a direction. In the above figure, graph G2 is a directed graph.

**2. Undirected graph**: An undirected graph G is a graph in which each edge e is not assigned a directed. In the above figure, graph G is a undirected graph.

**3. Connected graph:** A graph ( not digraph) is called connected if there is a path from any vertex to any other vertex.

A graph G is connected if and only if there is a simple path between any two nodes in G. A graph G is said to be complete if every node U in G is adjacent to every other node V in G. A complete graph with n nodes has: n*{(n-1)/2} edges.

**4. Weighted graph:** A weighted graph is a graph in which edges are assigned weights. This is often required to model certain physical situations by means of a graph.

**5. Complete graph:** A graph (digraph) G is said to be complete if each vertex Vi is adjacent to every other vertex Vj in G. In other word, there are edges from any vertex to all other vertices.

** 6. Null Graph- **A graph which contains only isolated node is called a null graph i.e. set of edges in a null graph is empty.

**7. Regular Graph:** A graph in which all the vertices are of equal degree is called a regular graph. If the degree of each vertex is r, then the graph is called a regular graph of degree r.

Every null graph is a regular graph of degree zero and a complete graph Kn is a regular graph of degree n-1.

**8. Cyclic Graph** - A graph with continuous sequence of vertices and edges is called a cyclic graph.

Cyclic graph is denoted on ‘n’ vertices bt Cn where n >=3.

**9. Wheel Graph -** A graph formed by adding a vertex inside a cycle and connecting it to every other vertex is known as wheel graph.

Wheel graph is denoted on 'n' vertices bt Wn where n>=3.

**10. Bipartite Graph- **A graph G=(V,E) ia bipartite if the vertex set V can be partitioned into two subsets V1 and V2 such that every edge in E connects a vertex in V1 and a vertex in V2 (no edge in G connects either two vertices in V1 or two vertices in V2) is called a bipartite graph. A bipartite graph can have no loop.

**11. Complete Bipartite Graph -**A graph where a set of vertices of a graph can be partitioned into two subsets in such a way that no pair of vertices in the same set are adjacent to each other and every vertex of first set is adjacent to the second set.

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