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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.
Proof for Absolute Convergence Very first notice that |a n | is either a n or it is - a n depending upon its sign. The meaning of this is that we can then say, 0 a n +
An automobile manufacturer needs to build a data warehouse to store and analyze data about repairs of vehicles. Among other information, the date of repair, properties of the vehic
A bourbon that is 51 proof is 25.5% alcohol by volume while one that is 82 proof is 41% alcohol. How many liters of 51 proof bourbon must be mixed with 1.0 liter of 82 proof bourbo
Suppose a fluid (say, water) occupies a domain D? R^(3 ) and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid
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The operator of an amusement park game remain track of how many tries it took participants to win the game. The subsequent is the data from the ?rst ten people: 2, 6, 3, 4, 6, 2, 8
The law of cosines can only be applied to acute triangles. Is this true or false?
show that a*0=a
Graph f ( x ) = e x and g ( x ) = e - x . Solution There actually isn't a lot to this problem other than ensuring that both of these exponentials are graphed somewhere.
As1212uestion #Minimum 100 words accepted#
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