Chromatic Classes of 2-Connected (n,n+4)-Graphs with Exactly Three Triangles and at Least Two Induced 4-Cycles

For a graph G, let P(G,λ) be its chromatic polynomial. Two graphs G and H are chromatically equivalent, denoted G∼H, if P(G,λ)=P(H,λ). A graph G is chromatically unique if P(H,λ)=P(G,λ) implies that H≅G. In this paper, we determine all chromatic equivalence classes of 2-connected (n,n+4)-graphs with exactly three triangles and at least two induced 4-cycles. As a byproduct of these, we obtain various new families of χ-equivalent graphs and χ-unique graphs.