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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.
Example Show that p ( x ) = 2 x 3 - 5x 2 -10 x + 5 has a root somewhere in the interval [-1,2]. Solution What we're actually asking here is whether or not the function wi
Determine the inverse of the following matrix, if it exists. We first form the new matrix through tacking onto the 3 x 3 identity matrix to this matrix. It is, We
lnx(1+x)
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one bathroom is 0.3m long how long is a row of 8 tiles
Sketch the graph of h (t ) = 1 - 5e 1/(t/2) Solution : Let's primary get a table of values for this function. Following is the sketch. The major point behin
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