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.
Opuscula Mathematica - cover

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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