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$\begin{align*} &S = \left \{ G_i \;\; | \; G_i \in \text{ lebeled trees with 4 vertices} \right \} \\ &\text{Relation } \quad R = \left \{ {\color{red}{\left ( G_i,G_j \right )}} \; | G_i,G_j \in S \;\; \text{and} \;\; G_i,G_j \;\; \text{are} \;\; \text{isomorphic to each other} \right \} \end{align*}$

No of equivalent classes of $R$ ?
asked in Combinatory by Veteran (50.9k points)  
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How come you are comparing trees? For isomorphism, the labels must also be same, right?
Sir is isomorphism is checked only in terms of their structure? Shouldn't it be checked for adjacent colors also?
@debashish,i thought the answer is only 1 as we can get tree with nonly 3 edges
so,you are saying that first 12 are in one class of isomorphism,

whya bove 12 not isomorphic to bottom 4??

is it because there degrees are different..right??
Yes first see no. Of vertices and edges, then check for degree sequence then check for same cycle length. 2 equivalence classes. Btw good question.

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