Chromaticity of certain tripartite graphs identified with a path

• Published in: Discrete Mathematics
• Main Author: Lau G.C.; Peng Y.H.
• Format: Article
• Language: English
• Published: 2006
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-33749251616&doi=10.1016%2fj.disc.2006.05.029&partnerID=40&md5=a0d884d6937462a98ad5170f59d1bdfb

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.