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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.
Define Markov chain Random processes with Markov property which takes separate values, whether t is discrete or continuous, are known as Markov chains.
-1+5-100=?
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The base and corresponding altitude of a parallelogram are 10 cm and 12 cm reap. If the other altitude is 8 cm , find the length of the other pair of parallel side
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The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3 times the length. Find out the width of the rectangle. Let l = the length of the rectangle and let
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