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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.
Given two functions f(x) and g(x) which are differentiable on some interval I (1) If W (f,g) (x 0 ) ≠ 0 for some x 0 in I, so f(x) and g(x) are linearly independent on the int
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core competency vs diversification
whta are the formulas needed for proving in trignometry .
Subjective Probability Probability may be determined by a personal statement of how likely an outcome is in a single trial or repetition of the same experiment. Since sub
A man can do a piece of work in 25 days how many people are required to complete same work in 15 days?
Determine or find out if the subsequent series is convergent or divergent. If it converges find out its value. Solution To find out if the series is convergent we fir
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Variance Square of the standard deviation is termed as variance. The semi inter-quartile range - It is a measure of dispersion which includes the use of quartile. A q
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