IJPAM: Volume 85, No. 1 (2013)

CHROMATIC EQUIVALENCE OF A FAMILY OF
K4-HOMEOMORPHS WITH GIRTH 9

Roslan Hasni
Department of Mathematics
Faculty of Science and Technology
University Malaysia Terengganu
21030, Kuala Terengganu, Terengganu, MALAYSIA


Abstract. For a graph G, let P(G,λ) denote the chromatic polynomial of G. Two graphs G and H are chromatically equivalent (or simply χ-equivalent), denoted by G\sim H, if P(G,\l)=P(H,\l). A graph G is chromatically unique (or simply χ-unique) if for any graph H such as H\sim G, we have H\cong G, i.e, H is isomorphic to G. A K4-homeomorph is a subdivision of the complete graph K4. In this paper, we determine when two K4-homeomorphs of the form K4(2,3,4,d,e,f) and K4(1,2,6,d',e',f') are chromatically equivalent. The result obtained can be extended in the study of chromatic equivalence classes of K4(2,3,4,d,e,f) and chromatic uniqueness of K4-homeomorphs with girth 9.

Received: October 29, 2012

AMS Subject Classification: 05C15

Key Words and Phrases: chromatic polynomial, chromatic equivalence, K4-homeomorphs

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DOI: 10.12732/ijpam.v85i1.4 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 1