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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.
Find all the real solutions to cubic equation x^3 + 4x^2 - 10 =0. Use the cubic equation x^3 + 4x^2 - 10 =0 and perform the following call to the bisection method [0, 1, 30] Use
miaty and yesenia have a group of base ten blocks.Misty has six more than yesnia. Yesenia''s blocks repersent 17 together they have 22 blocks,and the total of blocks repersent 85.
81-3/4
4.2^2x+1 - 9.2^x + 1=0
a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k
HISTORY OF UNITARY METHOD
Taking 2^x=m and solving the quadratic for getting D>=0 we get range= [3/4 , infinity )
Impediments in time series analysis Accuracy of data in reflecting a) Drastic changes for illustration in the advent of a major competitor, period of war or unexpected chan
writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a
Particular to General : When I say 'tail', what do you think of? Do you think of the tail of a horse, or of a monkey? Or do you think of the tail of your pet dog? The tail of
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