Research Article
BibTex RIS Cite

On equitable chromatic number of Tadpole graph T_{m,n}

Year 2019, Volume: 68 Issue: 2, 1638 - 1646, 01.08.2019
https://doi.org/10.31801/cfsuasmas.546904

Abstract

Graph coloring is a special case of graph labeling. Proper vertex k-coloring of a graph Gis to color all the vertices of a graph with different colors in such a way that no two adjacent vertices are assigned with the same color. In a vertex coloring of G, the set of vertices with the same color is called color class. An equitable k-coloring of a graph G is a proper k-coloring in which any two color classes differ in size by atmost one. In this paper we give results regarding the equitable coloring of central, middle, total and line graphs of Tadpole graph which is obtained by connecting a cycle graph and a path graph with a bridge.

References

  • Akbar, Ali M.M. and Vernold, Vivin J., Harmonious chromatic number of central graph of complete graph families, Journal of Combinatorics Information and System Sciences, Vol.32, No 1-4 (Combined), (2007).
  • Akbar, Ali M.M, Kaliraj, K., and Vernold, Vivin J., On equitable coloring of central graphs and total graphs, Electronic notes in Discrete Mathematics, 33, (2009).
  • Bondy, J.A. and Murty, U.S.R., Graph theory with Applications, London, MacMillan, 1976.
  • Chen, B.L. and Lin, K.W., A note on the m--bounded chromatic number of a tree, Eur. J. Combia. 14(1994).
  • Furmanczyk, H., Equitable coloring of Graph products, Opuscula Mathematica, Vol 26. No.1, (2006).
  • Furmanczyk, H., Jastrzebski A, Kubale M, Equitable coloring of graphs, Recent theoretical results and new practical Algorithms.
  • Hajnal, A., Szemeredi E., Proof of a conjecture of Endos, in: Combinatorial theory and its applications, Colloq. Math. Soc. Janos Bolyai, North - Holland, Amsterdam, Vol - 4, II, (1970), 601 - 623.
  • Hansen, P., Hertz A, and Kuplinsky J, Bounded vertex colorings of graphs, Discrete Math 111, (1993).
  • Meyer, W., Equitable coloring, Amer. Math. Monthly, 80, (1973).
  • Yan, Z., Wang, W., Equitable chromatic threshold of complete multipartite graphs, Combinatorics, (2012).
Year 2019, Volume: 68 Issue: 2, 1638 - 1646, 01.08.2019
https://doi.org/10.31801/cfsuasmas.546904

Abstract

References

  • Akbar, Ali M.M. and Vernold, Vivin J., Harmonious chromatic number of central graph of complete graph families, Journal of Combinatorics Information and System Sciences, Vol.32, No 1-4 (Combined), (2007).
  • Akbar, Ali M.M, Kaliraj, K., and Vernold, Vivin J., On equitable coloring of central graphs and total graphs, Electronic notes in Discrete Mathematics, 33, (2009).
  • Bondy, J.A. and Murty, U.S.R., Graph theory with Applications, London, MacMillan, 1976.
  • Chen, B.L. and Lin, K.W., A note on the m--bounded chromatic number of a tree, Eur. J. Combia. 14(1994).
  • Furmanczyk, H., Equitable coloring of Graph products, Opuscula Mathematica, Vol 26. No.1, (2006).
  • Furmanczyk, H., Jastrzebski A, Kubale M, Equitable coloring of graphs, Recent theoretical results and new practical Algorithms.
  • Hajnal, A., Szemeredi E., Proof of a conjecture of Endos, in: Combinatorial theory and its applications, Colloq. Math. Soc. Janos Bolyai, North - Holland, Amsterdam, Vol - 4, II, (1970), 601 - 623.
  • Hansen, P., Hertz A, and Kuplinsky J, Bounded vertex colorings of graphs, Discrete Math 111, (1993).
  • Meyer, W., Equitable coloring, Amer. Math. Monthly, 80, (1973).
  • Yan, Z., Wang, W., Equitable chromatic threshold of complete multipartite graphs, Combinatorics, (2012).
There are 10 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

K. Praveena This is me 0000-0002-5527-7600

M. Venkatachalam 0000-0001-5051-4104

Publication Date August 1, 2019
Submission Date February 5, 2018
Acceptance Date June 28, 2018
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Praveena, K., & Venkatachalam, M. (2019). On equitable chromatic number of Tadpole graph T_{m,n}. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1638-1646. https://doi.org/10.31801/cfsuasmas.546904
AMA Praveena K, Venkatachalam M. On equitable chromatic number of Tadpole graph T_{m,n}. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1638-1646. doi:10.31801/cfsuasmas.546904
Chicago Praveena, K., and M. Venkatachalam. “On Equitable Chromatic Number of Tadpole Graph T_{m,n}”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1638-46. https://doi.org/10.31801/cfsuasmas.546904.
EndNote Praveena K, Venkatachalam M (August 1, 2019) On equitable chromatic number of Tadpole graph T_{m,n}. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1638–1646.
IEEE K. Praveena and M. Venkatachalam, “On equitable chromatic number of Tadpole graph T_{m,n}”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1638–1646, 2019, doi: 10.31801/cfsuasmas.546904.
ISNAD Praveena, K. - Venkatachalam, M. “On Equitable Chromatic Number of Tadpole Graph T_{m,n}”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1638-1646. https://doi.org/10.31801/cfsuasmas.546904.
JAMA Praveena K, Venkatachalam M. On equitable chromatic number of Tadpole graph T_{m,n}. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1638–1646.
MLA Praveena, K. and M. Venkatachalam. “On Equitable Chromatic Number of Tadpole Graph T_{m,n}”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1638-46, doi:10.31801/cfsuasmas.546904.
Vancouver Praveena K, Venkatachalam M. On equitable chromatic number of Tadpole graph T_{m,n}. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1638-46.

Cited By

On the r-dynamic coloring of some fan graph families
Analele Universitatii "Ovidius" Constanta - Seria Matematica
https://doi.org/10.2478/auom-2021-0039

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.