Define complete graph and complete bipartite graph. Draw a graph which is a complete graph as well asa complete bipartite graph.
Question
Define complete graph and complete bipartite graph. Draw a graph which is a complete graph as well as a complete bipartite graph.
Solution
To define a complete graph, we can say that it is a simple undirected graph in which every pair of distinct vertices is connected by an edge. In other words, in a complete graph, there is an edge between every pair of vertices.
A complete bipartite graph, on the other hand, is a bipartite graph in which every vertex in one set is connected to every vertex in the other set. In other words, it is a graph that can be divided into two sets of vertices, and there is an edge between every vertex in one set and every vertex in the other set.
Now, let's draw a graph that is both a complete graph and a complete bipartite graph. We can achieve this by having two sets of vertices, let's say set A and set B. In set A, we have three vertices, let's label them as A1, A2, and A3. In set B, we also have three vertices, let's label them as B1, B2, and B3.
To make it a complete graph, we need to connect every pair of vertices. So, we draw edges between A1 and A2, A1 and A3, A2 and A3, B1 and B2, B1 and B3, and B2 and B3.
To make it a complete bipartite graph, we need to connect every vertex in set A to every vertex in set B. So, we draw edges between A1 and B1, A1 and B2, A1 and B3, A2 and B1, A2 and B2, A2 and B3, A3 and B1, A3 and B2, and A3 and B3.
By doing this, we have created a graph that is both a complete graph and a complete bipartite graph.
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