Table of Contents
ISRN Discrete Mathematics
Volume 2011, Article ID 430396, 15 pages
Research Article

Chromatic Classes of 2-Connected (𝑛,𝑛+4)-Graphs with Exactly Three Triangles and at Least Two Induced 4-Cycles

1Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Johor Campus, Segamat, Malaysia
2Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Malaysia

Received 7 July 2011; Accepted 15 August 2011

Academic Editor: G. Isaak

Copyright © 2011 G. C. Lau and Y. H. Peng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a graph 𝐺, let 𝑃(𝐺,πœ†) be its chromatic polynomial. Two graphs 𝐺 and 𝐻 are chromatically equivalent, denoted 𝐺∼𝐻, if 𝑃(𝐺,πœ†)=𝑃(𝐻,πœ†). A graph 𝐺 is chromatically unique if 𝑃(𝐻,πœ†)=𝑃(𝐺,πœ†) implies that 𝐻≅𝐺. In this paper, we determine all chromatic equivalence classes of 2-connected (𝑛,𝑛+4)-graphs with exactly three triangles and at least two induced 4-cycles. As a byproduct of these, we obtain various new families of πœ’-equivalent graphs and πœ’-unique graphs.