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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.
find probability
Test of hypothesis about the population mean When the population standard deviation (S) is identified then the t statistic is defined as t = ¦(x¯ - µ)/ S x¯ ¦
Steve earned a 96 percent on his ?rst math test, a 74% on his second test, and an 85 percent on his third test. What is his test average? Add the test grades (96 + 74 + 85 = 25
2x=3+x
If we "break up" the root into the total of two pieces clearly we get different answers. Simplified radical form: We will simplify radicals shortly so we have to next
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-9+f ?-1 ?? (a-1)=-12 f(-3)=2
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i want some assignment for earning i am mathematics expert plz provide us mathematics assignment as soon as possible
GENERAL RULE A general rule is to subtract the probabilities with an even number of components inside the parentheses and add those with an odd number of components (one or th
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