Opuscula Math. 30, no. 2 (2010), 123-131
http://dx.doi.org/10.7494/OpMath.2010.30.2.123

Opuscula Mathematica

# On chromatic equivalence of a pair of K4-homeomorphs

S. Catada-Ghimire
H. Roslan
Y. H. Peng

Abstract. Let $$P(G, \lambda)$$ be the chromatic polynomial of a graph $$G$$. Two graphs $$G$$ and $$H$$ are said to be chromatically equivalent, denoted $$G \sim H$$, if $$P(G, \lambda) = P(H, \lambda)$$. We write $$[G] = \{H| H \sim G\}$$. If $$[G] = \{G\}$$, then $$G$$ is said to be chromatically unique. In this paper, we discuss a chromatically equivalent pair of graphs in one family of $$K_4$$-homeomorphs, $$K_4(1, 2, 8, d, e, f)$$. The obtained result can be extended in the study of chromatic equivalence classes of $$K_4(1, 2, 8, d, e, f)$$ and chromatic uniqueness of $$K_4$$-homeomorphs with girth $$11$$.

Keywords: chromatic polynomial, chromatic equivalence, $$K_4$$-homeomorphs.

Mathematics Subject Classification: 05C15.

Full text (pdf)

• S. Catada-Ghimire
• Universiti Sains Malaysia, School of Mathematical Sciences, 11800 Penang, Malaysia
• H. Roslan
• Universiti Sains Malaysia, School of Mathematical Sciences, 11800 Penang, Malaysia
• Y. H. Peng
• Universiti Putra Malaysia, Department of Mathematics and Institute for Mathematical Research, 43400UPM Serdang, Malaysia
• Received: 2008-09-24.
• Revised: 2010-01-08.
• Accepted: 2010-01-08.

Cite this article as:
S. Catada-Ghimire, H. Roslan, Y. H. Peng, On chromatic equivalence of a pair of K4-homeomorphs, Opuscula Math. 30, no. 2 (2010), 123-131, http://dx.doi.org/10.7494/OpMath.2010.30.2.123

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