| Summary: | For a graph G, let P (G) be its chromatic polynomial. Two graphs G and H 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 - 2 e) ∪ Pm (m ≥ 6) by identifying the end-vertices of the path Pm with any two vertices of K2, 2, 2, K2, 2, 2 - e and K2, 2, 2 - 2 e, respectively, where e and 2 e are, respectively, an edge and any two edges of K2, 2, 2. As a by-product of this, we obtain some families of chromatically unique and chromatically equivalent classes of graphs. © 2006 Elsevier B.V. All rights reserved.
|
|---|