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Question

Let G = (V,E) be a graph. Define ξ(G) = Σd id x d, where id is the number of vertices of degree d in G. If S and T are two different trees with ξ(S) = ξ(T),then

a.

|S| = 2|T|

b.

|S| = |T|-1

c.

|S| = |T|

d.

|S| = |T|+1

Answer: (c).|S| = |T|

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Q. Let G = (V,E) be a graph. Define ξ(G) = Σd id x d, where id is the number of vertices of degree d in G. If S and T are two different trees with ξ(S) = ξ(T),then

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