Chromatic classes of 2-connected \((n,n+3)\)-graphs with at least two triangles (Q1322232)

Two graphs \(G\) and \(H\) are said to be chromatically equivalent if their chromatic polynomials are the same. A graph \(G\) is said to be chromatically unique if every graph chromatically equivalent to \(G\) is isomorphic to \(G\). Let \(C\) denote the class of all 2-connected graphs of order \(n\) and size \(n+3\) having at least two 3-cycles. In this paper all equivalence classes in \(C\) under the equivalence relation of chromatic equivalence are determined; the structure of the graphs in each class is characterized; new families of chromatically equivalent and chromatically unique graphs are produced.