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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.
If a school has lockers with 50 numbers on each combination lock, how many possible combinations using three numbers are there.
Example1 : Solve the subsequent system of equations. -2x 1 + x 2 - x 3 = 4 x 1 + 2x 2 + 3x 3 = 13 3x 1 + x 3 = -1 Solution The initial step is to write d
Evaluate the mean of temperatures: Example: Given the subsequent temperature readings, 573, 573, 574, 574, 574, 574, 575, 575, 575, 575, 575, 576, 576, 576, 578 So
Q) In a lottery ,a person chooses six different natural numbers at random 1to 20,and if there six numbers match with the six numbers already fixed by the lottery committee ,he win
Differentiate following. f ( x ) = sin (3x 2 + x ) Solution It looks as the outside function is the sine & the inside function is 3x 2 +x. The derivative is then.
any tutorials?
detail on identity function
The first particular case of first order differential equations which we will seem is the linear first order differential equation. In this section, unlike many of the first order
Whats some negative integers that equal 36
51/6 divided by 31/3
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