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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.
A computer is programmed to scan the digits of the counting numbers.For example,if it scans 1 2 3 4 5 6 7 8 9 10 11 12 13 then it has scanned 17 digits all together. If the comput
The light on a lighthouse blinks 45 times a minute. How long will it take the light to blink 405 times? Divide 405 by 45 to get 9 minutes.
4.4238/[1.047+{1.111*[9.261/7.777]}*1.01
Evaluate the subsequent inverse trigonometric functions: Evaluate the subsequent inverse trigonometric functions. arcsin 0.3746 22° arccos 0.3746 69° arctan 0.383
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Find the sum og series 1+(1+3)+(1+3+5)+.......+(1+3+...+15+17)=
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