TY  - JOUR
ID  - CatadaGhimire2010
LB  - CatadaGhimire2010
AU  - Catada-Ghimire, S.
AU  - Roslan, H.
AU  - Peng, Y. H.
TI  - On chromatic equivalence of a pair of K<sub>4</sub>-homeomorphs
ST  - On chromatic equivalence of a pair of K<sub>4</sub>-homeomorphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 2
SP  - 123
EP  - 131
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.2.123
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.2.123
AB  - 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 \(11\).
KW  - chromatic polynomial
KW  - chromatic equivalence
KW  - \(K_4\)-homeomorphs
SN  - 1232-9274
ER  -