TITLE: Graphs with the same chromatic symmetric function
QUESTION [10 upvotes]: Does anyone know more examples of two nonisomorphic connected graphs with the same chromatic symmetric function?  The only pair I know is the one in Stanley's paper on c.s.f.'s [http://math.mit.edu/~rstan/pubs/pubfiles/100.pdf; p.5 of the PDF file].  I would especially like to have an example in which at least one of the two graphs is triangle-free.

REPLY [5 votes]: This is quite an old post of mine.  Subsequently, Rosa Orellana and Geoffrey Scott gave an infinite family of pairs of unicyclic graphs with the same chromatic symmetric functions [Discrete Math. 320 (2014), 1–14].  That's the best answer to this question that I know of.  Stanley's original question for trees is still (frustratingly) open, so far as I know.