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Computer Science (GATE Exam) 2010 - Previous Question Paper Solution

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Multiple Choice

Let G=(V, E) be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in G. If S and T are two different trees with $\xi(S) = \xi(T)$, then

  1. $\mid$S$\mid$ = 2$\mid$T$\mid$
  2. $\mid$S$\mid$ = $\mid$T$\mid$ - 1
  3. $\mid$S$\mid$ = $\mid$T$\mid$
  4. $\mid$S$\mid$ = $\mid$T$\mid$ + 1
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