distributive property

Question

If suppose we take 3 vertices of a graph to check if it satisfies distributive property

 

atleast one vertice of that graph has unique compliment then it will satisfy distributive property

 

is this assumption correct ?

 

if not can i have an counter example

Comments

by book the definition is 'if there is a complement,that should be unique' in case of distributive lattices.There can be some element where there might not be any complement at all,but is still distributive.

But what you are asking is whether if there is no unique complement for any element does it satisfy distribution or not.This is somewhat ambigious to me,I dont have any counter example,let me work out if I find any.

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@surajit

no am asking if there is a unique complement for atleast one element then will it satisfy

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I think so...but you should not conclude its distribution property with just one element.Still I am not completely sure about this until I can prove it or find some proof.