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Though, there are a lot of different types of graphs depending upon the number of vertices, number of edges, interconnectivity, and their overall structure, some of such common types of graphs are as follows:
Example:
A null graph with n vertices is denoted by Nn.
Example:
In the above graph, there is only one vertex 'v' without any edge. Therefore, it is a trivial graph.
Example:
In the above example, First graph is not a simple graph because it has two edges between the vertices A and B and it also has a loop.
Second graph is a simple graph because it does not contain any loop and parallel edges.
Example:
In the above graph since there is no directed edges, therefore it is an undirected graph.
Example:
In the above graph, each edge is directed by the arrow. A directed edge has an arrow from A to B, means A is related to B, but B is not related to A.
Example:
In the above example, since each vertex in the graph is connected with all the remaining vertices through exactly one edge therefore, both graphs are complete graph.
Example:
In the above example, we can traverse from any one vertex to any other vertex. It means there exists at least one path between every pair of vertices therefore, it a connected graph.
Example:
The above graph consists of two independent components which are disconnected. Since it is not possible to visit from the vertices of one component to the vertices of other components therefore, it is a disconnected graph.
Example:
In the above example, all the vertices have degree 2. Therefore they are called 2 Regular graph.
Example 1:
In the above example, all the vertices have degree 2. Therefore they all are cyclic graphs.
Example 2:
Since, the above graph contains two cycles in it therefore, it is a cyclic graph.
Example:
Since, the above graph does not contain any cycle in it therefore, it is an acyclic graph.
Example 1:
Example 2:
Example:
The above graph is known as K4,3.
Example:
In the above example, out of n vertices, all the (n1) vertices are connected to a single vertex. Hence, it is a star graph.
Example:
In the above graph, if path is a > b > c > d > e > g then the length of the path is 5 + 4 + 5 + 6 + 5 = 25.
Example:
In the above graph, vertexset B and C are connected with two edges. Similarly, vertex sets E and F are connected with 3 edges. Therefore, it is a multi graph.
Example:
The above graph may not seem to be planar because it has edges crossing each other. But we can redraw the above graph.
The three plane drawings of the above graph are:
The above three graphs do not consist of two edges crossing each other and therefore, all the above graphs are planar.
Example:
The above graph is a non  planar graph.
47 videos119 docs75 tests

47 videos119 docs75 tests
