Chromatic classes of 2-connected -graphs with three triangles and one induced 4-cycle

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 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.