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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.
Basic "computation" formulas : Next, let's take a quick look at some basic "computation" formulas that will let us to actually compute some derivatives. Formulas 1) If f
Write down the first few terms of each of the subsequent sequences. 1. {n+1 / n 2 } ∞ n=1 2. {(-1)n+1 / 2n} ∞ n=0 3. {bn} ∞ n=1, where bn = nth digit of ? So
Mark is preparing a walkway around his inground pool. The pool is 20 by 40 ft and the walkway is intended to be 4 ft wide. Determine the area of the walkway? a. 224 ft 2 b.
What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems
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Find the series solution of2x2y”+xy’+(x2-3)Y=0 about regular singular pointuestion..
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two circle of radius of 2cm &3cm &diameter of 8cm dram common tangent
Illustration 1 In a described exam the scores for 10 students were given as: Student Mark (x) |x-x¯| A 60
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