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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.
what is -6.4 as a fraction?
using the formula sin A =under root 1+ cos2A /2 . find value of 30 degree, it is being given that cos 60 degree =1/2.
1. In an in finite horizon capital/consumption model, if kt and ct are the capital stock and consumption at time t, we have f(kt) = ct+kt+1 for t ≥ 0 where f is a given production
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Diffrent type of rectillinar figure..
JUST IS WHOLE
If a country with a struggling economy is losing the battle of the marketplace, should the affected government adjust its trade barriers to tilt the economic advantage of its domes
cos30 is equal to what?
EXPLAIN HOW MARKOV PROCESS IS APPLIED IN BRAND SWITCHING?
Differentiate following functions. h (t ) = 2t 5 + t 2 - 5 / t 2 We can simplify this rational expression as follows. h (t )
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