# co.combinatorics – Relation between two conjectures on reconstruction of graphs Answer

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co.combinatorics – Relation between two conjectures on reconstruction of graphs

In spectral graph concept, there’s a surmise that claims: Almost each graph is clear by its adjacency spectrum ($$DS$$). This surmise belongs to professor Willem Haemers.

Also, we’ve got a outcome by professor Béla Bollobás that claims: Almost each graph has reconstruction quantity three ($$RC=$$ Almost each graph is reconstructible).

We have a theorem in spectral graph concept that claims: We can assemble the attribute polynomial of a graph by its deck. I’ve two questions:

$$1)$$ Can we are saying one thing love that: Almost each graph has a attribute polynomial reconstruction quantity $$ok < n$$? For instance $$ok=3$$.
By attribute polynomial reconstruction quantity $$3$$, I denote if we’ve got a $$3$$ apt graphs within the deck of the unique graph, we will secure its attribute polynomial.

$$2)$$ What is the issue if we are saying that $$RCrightarrow DS$$ or $$DSrightarrow RC$$? Is it as a result of we labor with the phrases “Almost every …”?

Thank you in forward.

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