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January 12th, 2014, 01:52 PM   #1
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A graph problem in graph theory!

Please could anyone help me with the question.

Let G(E,V) be a graph with 32 edges. Suppose all the nodes have the same degree, let us call it d. What is the maximum size for this common degree d if the graph is connected?
(Hint: In any graph, the sum of the degrees of the nodes = twice the number of edges . Since all nodes have the same degree d, the sum of the degrees = nd = 32*2=64, where n = the number of nodes V. Now try values of d consistent with this. Do they all make sense, keeping in mind that nd = 64 ?)
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