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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.
Inverse Cosine : Now see at inverse cosine. Following is the definition for the inverse cosine. y = cos -1 x ⇔ cos y = x for
If the expression 9y - 5 represents a certain number, which of the following could NOT be the translation? a. five less than nine times y b. five less than the sum of 9 and y c
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how to work out consumer arithmetic?
1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
Q. Basic Set Union Operation? Ans. Suppose instead that your school needs to know which students are taking either art or business or both. Then the students who are ta
a sail has a spread of canvas as measured 12'',12'', 15'' and 9'' and it has 90 degrees. Find the area of one side of the sail
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i need help for DIFFERENTIAL EQUATION PROJECT
2 times n times n divided by n
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