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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.
1 1 1 1 1 2 1 2 ? and 40/2=? 2/40=?
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Sir before I applied for online assignment help job and the selection process is not complete for me. You sent me problem assignment before.But those problems were not completed.Ca
#quesSuppose we have a stick of length L. We break it once at some point X ~ Unif(0;L). Then we break it again at some point Y ~ Unif(0;X). Use the law of iterated expectation to c
A drug has a decay rate of k = - ¼ ln(¾) / hr. How soon after an initial dose of 1600 mg will the drug reach its minimum therapeutic value of 900 mg in the body?
in 2000,nearly 18% of cars in north America were sliver. what percent of the cars sold were not sliver?
Marketing management,Analysis,planning and implementation
Formulas
A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litres of 40% acid solution.
#The digits 1,2,3,4and 5 are arranged in random order,to form a five-digit number. Find the probability that the number is a. an odd number. b.less than 23,000
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