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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.
Mike, Dan, Ed, and Sy played together on a baseball team. Mike's batting average was 0.349, Dan's was 0.2, Ed's was 0.35, and Sy's was 0.299. Who had the highest batting average?
why we use decision making using minimization of regret method in uncertainty?
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The length of Kara's rectangular patio can be expressed as 2x - 1 and the width can be expressed as x + 6. In the terms of x, what is the area of her patio? Since the area of a
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Describe Adding and Subtracting Fractions in details? To add or subtract fractions, here are some steps: 1. Find the lowest common denominator (LCD) or any common denominato
1. Consider a source with 4 symbols {a,b,c,d}. The probability of the 4 symbols are P(a)=0.4, p(b) = 0.1, p(c)=0.2, p(d)= 0.3. a. Design a Huffman codebook for these symbols.
Look on the web for a data base that can be converted to an undirected graph. For example, in Science there is a data base of proteins and their interactions. Each protein can b
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how to express 15/4 into percentage
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