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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.
Connecticut state sales tax is 6%. Lucy purchases a picture frame in which costs $10.50 What is the Connecticut sales tax on this item? Find out 6% of $10.50 by multiplying $10
how do we figure it out here is an example 3,4,6,9,_,_,_,_,_,. please help
show that the subtangent at any point on parabola y2 =4ax is twice the abscissa at that point.
This problem involves the question of computing change for a given coin system. A coin system is defined to be a sequence of coin values v1 (a) Let c ≥ 2 be an integer constant
if theta is a positive acute angle and 2sin theta +15cos square theta=7 then find the value of cot theta
Q. What is a percentage? Ans. Percent means "per hundred", or "out of 100". A percentage can be written as a ratio, or fraction, where the denominator (bottom) is 100.
limit x APProaches infinity (1+1/x)x=e
how to Multiplying Rational Expressions ? To multiply fractions, or rational expressions, you must multiply the numerators and then multiply the denominators. Here's how it is
prove:
I have no clue how to do it
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