Which complete bipartite graphs are complete graphs

Graph Theory. Types of Graphs- Before you go through this article, make sure that you have gone through the previous article on various Types of Graphs in Graph Theory. Bipartite Graph in Graph Theory- A Bipartite Graph is a special graph that consists of 2 sets of vertices X and Y where vertices only join from one set to other.

Bipartite Graph Example. Bipartite Graph Properties are discussed. Akshay Singhal. We will discuss only a certain few important types of graphs in this chapter. Hence it is a Null Graph. Hence it is a Trivial graph. Similarly other edges also considered in the same way. As it is a directed graph, each edge bears an arrow mark that shows its direction. In the following graph, there are 3 vertices with 3 edges which is maximum excluding the parallel edges and loops.

This can be proved by using the above formulae. A graph G is said to be connected if there exists a path between every pair of vertices. There should be at least one edge for every vertex in the graph. So that we can say that it is connected to some other vertex at the other side of the edge. In the following graph, each vertex has its own edge connected to other edge.

Hence it is a connected graph. The two components are independent and not connected to each other. Hence it is called disconnected graph. In this example, there are two independent components, a-b-f-e and c-d, which are not connected to each other. A Euler Path through a graph is a path whose edge list contains each edge of the graph exactly once.

Euler Circuit: An Euler Circuit is a path through a graph, in which the initial vertex appears a second time as the terminal vertex. A Euler Circuit uses every edge exactly once, but vertices may be repeated.

Example: The graph shown in fig is a Euler graph. Determine Euler Circuit for this graph. Then we have two cases, graphs of which are shown in fig:. Induction Step: Let us assume that the formula holds for connected planar graphs with K edges.

Firstly, we suppose that G contains no circuits. Now, take a vertex v and find a path starting at v. Since G is a circuit free, whenever we find an edge, we have a new vertex. At last, we will reach a vertex v with degree1. So we cannot move further as shown in fig:. Now remove vertex v and the corresponding edge incident on v. Hence, the formula also holds for G.

Now, as e is the part of a boundary for two regions. Hence the formula also holds for G which, verifies the inductive steps and hence prove the theorem. JavaTpoint offers too many high quality services. Mail us on [email protected] , to get more information about given services. Please mail your requirement at [email protected] Duration: 1 week to 2 week.

Discrete Mathematics. Binary Operation Property of Binary Operations. Reinforcement Learning. R Programming. React Native. Python Design Patterns.