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 ‘ ∼’. ...

Let P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, written G∼H , if P(G) = P(H). A graph G is chromatically unique if for any graph H , G∼H implies that G is isomorphic with H . In this paper, we give the necessary and su:cient conditions for a family of generalized polygon trees to be chromatically unique. c © 2001 Elsevier Science B.V. All ...

A sunflower hypergraph SH(n, p, h) is an h-hypergraph of order n = h + (k − 1)p and size k (1 p h − 1 and h 3), where each edge (or a “petal”) consists of p distinct vertices and a common subset to all edges with h−p vertices. In this paper, it is shown that this hypergraph is h-chromatically unique (i.e., chromatically unique in the set of all h-hypergraphs) for every 1 p h − 2, but this is no...

Let P (G,λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G ∼ H, if P (G,λ) = P (H,λ). We write [G] = {H |H ∼ G}. If [G] = {G}, then G is said to be chromatically unique. A K4-homeomorph denoted by K4(a, b, c, d, e, f) if the six edges of complete graph K4 are replaced by the six paths of length a, b, c, d, e, f respectively. In th...

For a graphG, let P(G) be its chromatic polynomial. Two graphsG andH are chromatically equivalent if P(G)=P(H). A graph G is chromatically unique if P(H)= P(G) implies that H G. In this paper, we classify the chromatic classes of graphs obtained from K2,2,2 ∪ Pm(m 3), (K2,2,2 − e) ∪ Pm(m 5) and (K2,2,2 − 2e) ∪ Pm(m 6) by identifying the end-vertices of the path Pm with any two vertices of K2,2,...

For a graph G, let P (G,λ) denote the chromatic polynomial of G. Two graphs G and H are chromatically equivalent (or simply χ−equivalent), denoted by G ∼ H, if P (G,λ) = P (H,λ). A graph G is chromatically unique (or simply χ−unique) if for any graph H such as H ∼ G, we have H ∼= G, i.e, H is isomorphic to G. A K4-homeomorph is a subdivision of the complete graph K4. In this paper, we discuss a...