I have searched and searched and am unable to find the answer that I am looking for. I am trying to determine the conditions required for two graphs to have the same chromatic polynomial.
On both Wikipedia and Wolfram MathWorld it states that two graphs are chromatically equivalent if they have the same chromatic polynomial. It then gives a few known chromatically equivalent graphs. But I don't believe this really answers my question as what I want to know is what conditions exist that make those graphs have the same chromatic polynomial. For example, must they have the same number of vertices, the same number of edges, etc.
The book "Chromatic Polynomials and Chromaticity of Graphs" by F. M. Dong, Khee Meng Koh, and K. L. Teo has an entire chapter dedicated to results about chromatically equivalent graphs. See chapter 3, and particularly Theorem 3.2.1.
http://books.google.com/books?id=bvhpExuQcq8C&pg=PA55&dq=chromatically+equivalent+graphs&source=gbs_toc_r&cad=4#v=onepage&q=chromatically%20equivalent%20graphs&f=false