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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.
how many times In a 12 hour period will he numbers add up to 6? (hint 3:00 is one answer0
This question has two related parts, (a) and (b). (a) Use the daily yields in the table below to compute a daily standard deviation of yields. Next annualize the daily standard
There isn't actually a whole lot to this section this is mainly here thus we can get several basic concepts and definitions out of the way. Most of the concepts and definitions in
Non Zero Sum Games Recently there was no satisfactory theory either to describe how people should play non-zero games or to explain how they actually play that game Nigel Ho
If the hight of pipe is 18 inches, what is the volume of the shaded region in terms of π? a. 31.5π in 3 b. 126π in 3 c. 157.5 in 3 d. 58.5 in 3
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y'' + 2y = 2 - e-4t, y(0) = 1 use euler''s method with a step size of 0.2 to find and approximate values of y
Properties of t distribution 1. The t distribution ranges from - ∞ to ∞ first as does the general distribution 2. The t distribution as the standard general distribution is
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