Chromatic classes of 2-connected (n, n+4)-graphs with three triangles and one induced 4-cycle

For a graphG, let P(G, λ)be its chromatic polynomial. TwographsG andH 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 shall determine all chromatic equivalence classes of 2-connected (n, n+ 4)-graphs with three triangles and one induced 4-cycle, under the equivalence relation ‘ ∼’. As a by product of these, we obtain various new families of chromatically-equivalent graphs and chromatically-unique graphs. © 2008 Elsevier B.V. All rights reserved.