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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.
I was never really good at mathematics what is the best way? I am reading Math better explained but is there anything else I can do? I want to study advanced topics and get a good
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Question: Classify the following differential equations as linear/nonlinear. Also, what is the order of the following differential equations? Xy'-2y =x Xy'' -2y' =xsin(y)
Write the doubles fact you used to solve the problem. 7 + 8 = 15
Suppose A and B be two non-empty sets then every subset of A Χ B describes a relation from A to B and each relation from A to B is subset of AΧB. Normal 0 fals
Suppose that x = x (t ) and y = y (t ) and differentiate the following equation with respect to t. Solution x 3 y 6 + e 1- x - cos (5
robin runs 5 kilometers around the campus in the same length of time as he can walk 3 kilometers from his house to school. If he runs 4 kilometers per hour faster than he walks, ho
compare 643,251;633,512; and 633,893. The answer is 633,512
When the son will be as old as the father today their ages will add up to 126 years. When the father was old as the son is today, their ages add upto 38 years. Find their present
what is 24566x12567=
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