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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.
When finding the limit as x approaches 0 the for function (square root of x^3 + x^2) cos(pi/2x) would the limit not exist because there would be a zero in the denominator?
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which of these is between 5,945,089 and 5,956,108
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Hi I have a maths question related to construction as its a construction management course...i could send some example sheets too...could it be done?
can i known the all equations under this lesson with explanations n examples. please..
log4^(x+2)=log4^8
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