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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.
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Differentiate y = x x Solution : We've illustrated two functions similar to this at this point. d ( x n ) /dx = nx n -1 d (a x ) /dx= a
1. Consider the following context free grammar G with start symbol S (we write E for the empty string, epsilon): S ---> bB | aSS A ---> aB | bAA B ---> E | bA | aS a. D
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a sail has a spread of canvas as measured 12'',12'', 15'' and 9'' and it has 90 degrees. Find the area of one side of the sail
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How do I reverse calculate taxes?
Write a function that computes the product of two matrices, one of size m × n, and the other of size n × p. Test your function in a program that passes the following two matrices t
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