[vlasev]

> "Every one of these graphs has a unique chromatic polynomial"

This is incorrect. Two different graphs may have the same chromatic polynomial. For example, all trees of N vertices have the same chromatic polynomial: x(x-1)^(N-1)

[soVeryTired]

I think they're trying to say that the graph uniquely determines the polynomial, rather than that the polynomial determines the graph. Or at least, that's how I read it. But I agree it's a bit ambiguous.

[JadeNB]

> > "Every one of these graphs has a unique chromatic polynomial"

> This is incorrect. Two different graphs may have the same chromatic polynomial. For example, all trees of N vertices have the same chromatic polynomial: x(x-1)^(N-1)

As soverytired (https://news.ycombinator.com/item?id=14697626) points out, you're refuting the claim that the graphs have distinct chromatic polynomials. To say that a graph has a unique chromatic polynomial means that it has only one, not that no other graph has the same one. (For example, (almost?) everyone has a unique biological mother.)