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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.
Q, Did you know that you can unreduce a fraction? Ans. Remember, you reduce a fraction by dividing the numerator and denominator by the same numbers. Here we divide
Which of the subsequent numbers is equivalent to 12.087? Zeros can be added to the end (right) of the decimal portion of a number without changing the value of the number; 12.
1) Let the Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8}. Suppose each outcome is equally likely. Compute the probability of event E = "an even number is selected". P(E) = 2) A s
112 in 8
Patrick has a rectangular patio whose length is 5 m less than the diagonal and a width which is 7 m less than the diagonal. If the field of his patio is 195 m 2 , what is the lengt
4562388/955
in a triangle angle a is 70 and angle b is 50 what is angle c.
Definition of a Function Now we need to move into the second topic of this chapter. Before we do that however we must look a quick definition taken care of.
there are 300 students in the sixth grade. if 40% of them were girls, how many boys were there?
Distance Traveled by Car - word problem: It takes a man 4 hours to reach a destination 1325 miles from his home. He drives to the airport at an average speed of 50 miles per h
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