Table of Contents
ISRN Discrete Mathematics
Volume 2011, Article ID 430396, 15 pages
http://dx.doi.org/10.5402/2011/430396
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.

Linked References

  1. C. Y. Chao and E. G. Whitehead Jr., β€œOn chromatic equivalence of graphs,” in Theory and Applications of Graph, Y. Alavi and D. R. Lick, Eds., vol. 642 of Lecture Notes in Mathematics, pp. 121–131, Springer, New York, NY, USA, 1978. View at Google Scholar
  2. B. Loerinc, β€œChromatic uniqueness of the generalized ΞΈ-graph,” Discrete Mathematics, vol. 23, no. 3, pp. 313–316, 1978. View at Google Scholar Β· View at Scopus
  3. F. M. Dong, K. L. Teo, and K. M. Koh, β€œA note on the chromaticity of some 2-connected (n,n+3)-graphs,” Discrete Mathematics, vol. 243, no. 1–3, pp. 217–221, 2002. View at Google Scholar Β· View at Scopus
  4. K. M. Koh and K. L. Teo, β€œChromatic classes of 2-connected (n,n+3)-graphs with at least two triangles,” Discrete Mathematics, vol. 127, no. 1–3, pp. 243–258, 1994. View at Google Scholar Β· View at Scopus
  5. K. L. Teo and K. M. Koh, β€œChromatic classes of certain 2-connected (n,n+2)-graphs,” Ars Combinatoria, vol. 32, pp. 65–76, 1991. View at Google Scholar
  6. Y. H. Peng and G. C. Lau, β€œChromatic classes of 2-connected (n,n+4)-graphs with at least four triangles,” Discrete Mathematics, vol. 278, no. 1–3, pp. 209–218, 2004. View at Publisher Β· View at Google Scholar Β· View at Scopus
  7. Y. H. Peng and G. C. Lau, β€œChromatic classes of 2-connected (n,n+4)-graphs with three triangles and one induced 4-cycle,” Discrete Mathematics, vol. 309, no. 10, pp. 3092–3101, 2009. View at Publisher Β· View at Google Scholar Β· View at Scopus
  8. G. C. Lau and Y. H. Peng, β€œRelative-closed family of graphs with exactly three triangles,” Technical Report 2, Institute for Mathematical Research, Putra, Malaysia, 2010. View at Google Scholar
  9. M. Behzad, G. Chartrand, and L. Lesniak-Foster, Graphs and Digraphs, Wadsworth, Belmont, Calif, USA, 1979.
  10. H. Whitney, β€œThe coloring of graphs,” Annals of Mathematics, vol. 33, pp. 688–718, 1932. View at Google Scholar
  11. A. A. Zykov, β€œOn some properties of linear complexes,” Matematicheskii Sbornik, vol. 24, pp. 163–188, 1949, Translation in American Mathematical Society Translations, no. 79. View at Google Scholar
  12. E. G. Whitehead Jr. and L. C. Zhao, β€œCutpoints and the chromatic polynomial,” Journal of Graph Theory, vol. 8, pp. 371–377, 1984. View at Google Scholar
  13. X. F. Li, β€œA family of chromatically unique K4-homeomorphs,” Journal of Anhui University of Technology and Science, vol. 32, no. 4, pp. 18–21, 2008. View at Google Scholar