On Chromatic Uniqueness of a Family of K₄-Homeomorphs II

Abstract

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 this paper, we study the chromatically unique of such K₄-homeomorph with girth 3a + 1, where b = a, c = a + 1 and d, e, f ≥ a.

Keywords:

• Chromatic polynomial
• Chromatic uniqueness
• K4-homeomorph

2010 Mathematics Subject Classification:

• Primary 05C15