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Show that the star graph is the only bipartiate graph which is a tree?
A star graph, call it S_k is a complete bipartite graph with one vertex in the center and k vertices around the leaves. To be a tree a graph on n vertices must be connected and have n-1 edges. We could also say it is connected and has no cycles. Now a star graph, say S_4 has 3 edges and 4 vertices and is clearly connected. It is a tree. This would be true for any S_k since they all have k vertices and k-1 edges. And Now think of K_1,k as a complete bipartite graph. We have one internal vertex and k vertices around the leaves. This gives us k+1 vertices and k edges total so it is a tree. So one way is clear. Now we would need to show that any bipartite graph other than S_1,k cannot be a tree. If we look at K_2,k which is a bipartite graph with 2 vertices on one side and k on the other,can this be a tree?
The similarities between a bar graph and a pie graph?
their both graphs
What similarities do you see between the graph of the reindeer population and your graph of the human population?
They both are increasing.
Why is tulip tree the sate tree of Indiana?
The tulip tree is the official state tree of Indiana. It is a tall tree and grows throughout Indiana.
What is the national tree in Algeria?
Hibiscus tree ! Yes , It is hibiscus tree .
