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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.
Coefficient of Correlation Denoted There are two methods which measure the degree of correlation among two variables these are denoted by R and r. (a) Coefficient of correl
6 male students and 3 female students sit around a round table. The probability that no 2 female students sit beside each other can be expressed as a/b, where a and b are coprime p
how can a curve be divided in three equal part?
a) The first comic book is of shakitman was sold in 1938. In 2010, the estimated price for this comic book in good condition was about $500,000. This represented a return of 25 per
definition and examples and types
There is a number. If the sum of digits is 14, and if 29 is subtracted from the number, the digits become equal. Find the number.
if one side of a square is increased 4 inches and an adjacement side is multiplied by 4, the perimeter of the resulting rectangle is 3 times the perimeter of the square. find the s
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Working Definition of Limit 1. We state that if we can create an as close to L like we want for all adequately large n. Alternatively, the value of the a n 's approach
Determine how many different words can be formed out of the letters of the word VARANASI? Ans: 720 different words can be formed out of the letters of the word VARANASI.
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