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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.
General approach of Exponential Functions : Before getting to this function let's take a much more general approach to things. Let's begin with b = 0 , b ≠ 1. Then an exponential f
Q. Sum and Difference Identities? Ans. These six sum and difference identities express trigonometric functions of (u ± v) as functions of u and v alone.
to use newspaper and report on share and dividend
-8 plus (-17)
0+50x1-60-60x0+10
a data set has a mean of 3, a median of 4, and a mode of 5.which number must be in the data set-3,4,5?
With a compass draw the arc associated with a 720° angle, it looks like a circle. With a protractor, label the angle in multiples of 45° and 30° up to 720°. Notice 30° and 390° ar
what is harmonic progression
Differentiate following functions. g ( x ) = 3sec ( x ) -10 cot ( x ) Solution : There actually isn't a whole lot to this problem. We'll just differentia
By using n = 4 and all three rules to approximate the value of the following integral. Solution Very firstly, for reference purposes, Maple provides the following valu
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