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Prove that a simple graph is connected if and only if it has a spanning tree.
Ans: First assume that a simple graph G has a spanning tree T. T consists of every node of G. By the definition of a tree, there is a path among any two nodes of T. As T is a subgraph of G, there is a path among each pair of nodes in G. Hence G is connected.
Here now let G is connected. If G is a tree then nothing to prove. If G is not a tree, it must consist of a simple circuit. Let G has n nodes. We can choose (n - 1) arcs from G in such type of a way that they not form a circuit. It results into a subgraph comprising all nodes and only (n - 1) arcs. So by definition this subgraph is a spanning tree.
vwertical and horizontal
2^(x) + 2^(x+3)=36
A boy covered half of distance at 20km/hr and rest at 40kmlhr. calculate his average speed.
Sherman took his pulse for 10 seconds and counted 11 beats. What is Sherman's pulse rate in beats per minute? A 10 second count is 1/6 of a minute. To find out the number of be
1/4 divided by (9/10 divided by 8/9)
What is a review technique? What are its advantages and disadvantages?
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