**1. Null Graph:** The graph which has no edges is known as Null Graph. Sometime it is also known as empty graph or edgeless graph.

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**2. Trivial Graph:** The graph which has only one vertex is known as Trivial Graph.

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**3. Non-Directed Graph:** These are the graphs that have edges with no direction.

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**4. Directed Graph:** These are the graph in which each edge has its direction.

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**5. Simple Graph:** These are undirected graph containing no graph loops or multiple edges. A simple graph can either be connected or disconnected.

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**6. Connected Graph:** The graph in which there is a path between every pair of vertices is called connected graph.

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**7. Disconnected Graph:** A graph G is said to be disconnected if it is not connected. If there exist two nodes in graph G such that no path in G has those nodes as endpoints.

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**8. Regular Graph:** The graph in which each vertex has same number of neighbours is called as regular graph.

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**9. Complete Graph:** A complete graph is a graph in which every pair of vertices is connected by an edge. A complete graph is simple undirected graph.

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**10. Cycle Graph:** The graph that is formed by connecting all the vertices together is known as cycle graph. The cycle graph with n vertices is called Cn.

If the degree of each vertex in a graph is 2 then that graph is said to be cycle graph.

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**11. Cyclic Graph:** The graph which contains at least one cycle in it then that graph is said to be cyclic graph.

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**12. Acyclic Graph:** The graph that contains no cycle in it is said to be Acyclic Graph.

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