Chia, G. L. and Ho, CheeKit * (2014) Chromatic equivalence classes of some families of complete tripartite graphs. Bulletin of the Malaysian Mathematical Sciences Society, 37 (3). pp. 641646.

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Abstract
We obtain new necessary conditions on a graph which shares the same chromatic polynomial as that of the complete tripartite graph Km,n,r. Using these, we establish the chromatic equivalence classes for K1,n,n+1 (where n ≥ 2). This gives a partial solution to a question raised earlier by the authors. With the same technique, we further show that Kn−3,n,n+1 is chromatically unique if n ≥ 5. In the more general situation, we show that if 2 ≤ m ≤ n, then Km,n,n+1 is chromatically unique if n is sufficiently large.
Item Type:  Article 

Additional Information:  First author is with the Institute of Mathematical Sciences, University of Malaya; second author is with the Dept. of Financial Mathematics and Statistics, Sunway University Business School 
Uncontrolled Keywords:  complete tripartite graph; chromatic polynomial; chromatic equivalence 
Subjects:  Q Science > QA Mathematics 
Divisions:  Sunway University > School of Mathematical Sciences > Department of Applied Statistics 
Depositing User:  Ms. Molly Chuah 
Date Deposited:  02 Apr 2015 14:34 
Last Modified:  13 Mar 2019 03:46 
URI:  http://eprints.sunway.edu.my/id/eprint/273 
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