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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.
Find the common difference of an AP whose first term is 100 and sum of whose first 6 terms is 5 times the sum of next 6 terms. Ans: a = 100 APQ a 1 + a 2 + ....... a 6
project
Perform each of the following algebraic expression as instruction says;- I.Multiply 5x+6m+4y by5 II.Divide 4ax+6ay-10az by 2a
2cos^2x-sinx=1......Find x
the probability that an account officer will pass her exam is 5/9. if she pass,the probability that she will be promoted is 3/4. she is not promoted if she fails her professional e
A man buys rs50 shares of a company paying 12% of dividendat premium ofof rs10 find market value of 320 shares and profit%
25/5(2+3)
Recognizes the absolute extrema & relative extrema for the given function. f ( x ) = x 3 on [-2, 2] Solution :
6 7/10+8 9/4
Give an example of Numerator and Denominator? Fractions represent parts of a whole object. Fractions are written using a horizontal line, with one number on top of the line and
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