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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.
Tchebyshev Distance (Maximum Travel Distance per Trip Using Rectilinear Distance): It can be calculated by using following formula: d(X, Pi) = max{|x - ai|, |y - bi|} (Source
A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all??
1. Give some Class 4 children around you problems like 15 x 6 to do dentally. Interact with them to find out the different strategies they use for doing it, and note these down.
Q. How to divide two fractions?If you want to divide two fractions, You invert the second fraction (that means, turn it upside-down) and multiply (change the division to a
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principal=2000 rate=5% time=2 years find compound interest
Q. Sum and Difference Identities? Ans. These six sum and difference identities express trigonometric functions of (u ± v) as functions of u and v alone.
The price of heating oil rose from $1.10 per gallon to $1.43 per gallon. What is the percent of increase? The price of heating oil rose $0.33 ($1.43 - $1.10 = $0.33). To ?nd ou
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problem set d, #7
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