Research Article
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Year 2018, Volume: 5 Issue: 1, 19 - 27, 15.01.2018
https://doi.org/10.13069/jacodesmath.349383

Abstract

References

  • [1] A. Banerjee, S. Bej, On extension of regular graphs, arXiv:1509.05476v1 [math.CO].
  • [2] J. A. Bondy, U. S. R. Murty, Graph Theory, Springer, 2008.
  • [3] S. Cabello, M. Jacovac, On the b–chromatic number of regular graphs, Discrete Appl. Math. 159 (2011) 1303–1310.
  • [4] G. Chartrand, L. Lesniak, Graphs and Digraphs, CRC Press, 2000.
  • [5] J. T. Gross, J. Yellen, Graph Theory and Its Applications, CRC Press, 2006.
  • [6] J. E. Hopcroft, R. M. Karp, An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs, SIAM J. Comput. 2(4) (1973) 225–231.
  • [7] J. Kok, N. K. Sudev, K. P. Chithra, Generalised colouring sums of graphs, Cogent Math. 3(1) (2016) 1–11.
  • [8] M. Kouider, A. El Sahili, About b–coloring of regular graphs, Rapport de Recherche, No. 1432, CNRS–Universite Paris Sud–LRI.
  • [9] E. Kubicka, A. J. Schwenk, An introduction to chromatic sums, Proc. ACM Computer Sci. Conf. (Louisville) (1989) 39–45.
  • [10] P. C. Lisna, M. S. Sunitha, b–chromatic sum of a graph, Discrete Math. Algorithm. Appl. 7(4) (2015) 1–15.
  • [11] N. K. Sudev, K. P. Chithra, J. Kok, Certain chromatic sums of some cycle-related graph classes, Discrete Math. Algorithm. Appl. 8(3) (2016) 1–25.

Coloring sums of extensions of certain graphs

Year 2018, Volume: 5 Issue: 1, 19 - 27, 15.01.2018
https://doi.org/10.13069/jacodesmath.349383

Abstract

We recall that the minimum number of colors that allow a proper coloring of graph $G$ is called the chromatic number of $G$ and denoted $\chi(G)$. Motivated by the introduction of the concept of the $b$-chromatic sum of a graph the concept of $\chi'$-chromatic sum and $\chi^+$-chromatic sum are introduced in this paper. The extended graph $G^x$ of a graph $G$ was recently introduced for certain regular graphs. This paper furthers the concepts of $\chi'$-chromatic sum and $\chi^+$-chromatic sum to extended paths and cycles. Bipartite graphs also receive some attention. The paper concludes with patterned structured graphs. These last said graphs are typically found in chemical and biological structures.

References

  • [1] A. Banerjee, S. Bej, On extension of regular graphs, arXiv:1509.05476v1 [math.CO].
  • [2] J. A. Bondy, U. S. R. Murty, Graph Theory, Springer, 2008.
  • [3] S. Cabello, M. Jacovac, On the b–chromatic number of regular graphs, Discrete Appl. Math. 159 (2011) 1303–1310.
  • [4] G. Chartrand, L. Lesniak, Graphs and Digraphs, CRC Press, 2000.
  • [5] J. T. Gross, J. Yellen, Graph Theory and Its Applications, CRC Press, 2006.
  • [6] J. E. Hopcroft, R. M. Karp, An $n^{5/2}$ algorithm for maximum matchings in bipartite graphs, SIAM J. Comput. 2(4) (1973) 225–231.
  • [7] J. Kok, N. K. Sudev, K. P. Chithra, Generalised colouring sums of graphs, Cogent Math. 3(1) (2016) 1–11.
  • [8] M. Kouider, A. El Sahili, About b–coloring of regular graphs, Rapport de Recherche, No. 1432, CNRS–Universite Paris Sud–LRI.
  • [9] E. Kubicka, A. J. Schwenk, An introduction to chromatic sums, Proc. ACM Computer Sci. Conf. (Louisville) (1989) 39–45.
  • [10] P. C. Lisna, M. S. Sunitha, b–chromatic sum of a graph, Discrete Math. Algorithm. Appl. 7(4) (2015) 1–15.
  • [11] N. K. Sudev, K. P. Chithra, J. Kok, Certain chromatic sums of some cycle-related graph classes, Discrete Math. Algorithm. Appl. 8(3) (2016) 1–25.
There are 11 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Johan Kok 0000-0003-0106-1676

Saptarshi Bej This is me

Publication Date January 15, 2018
Published in Issue Year 2018 Volume: 5 Issue: 1

Cite

APA Kok, J., & Bej, S. (2018). Coloring sums of extensions of certain graphs. Journal of Algebra Combinatorics Discrete Structures and Applications, 5(1), 19-27. https://doi.org/10.13069/jacodesmath.349383
AMA Kok J, Bej S. Coloring sums of extensions of certain graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. January 2018;5(1):19-27. doi:10.13069/jacodesmath.349383
Chicago Kok, Johan, and Saptarshi Bej. “Coloring Sums of Extensions of Certain Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 5, no. 1 (January 2018): 19-27. https://doi.org/10.13069/jacodesmath.349383.
EndNote Kok J, Bej S (January 1, 2018) Coloring sums of extensions of certain graphs. Journal of Algebra Combinatorics Discrete Structures and Applications 5 1 19–27.
IEEE J. Kok and S. Bej, “Coloring sums of extensions of certain graphs”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 5, no. 1, pp. 19–27, 2018, doi: 10.13069/jacodesmath.349383.
ISNAD Kok, Johan - Bej, Saptarshi. “Coloring Sums of Extensions of Certain Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications 5/1 (January 2018), 19-27. https://doi.org/10.13069/jacodesmath.349383.
JAMA Kok J, Bej S. Coloring sums of extensions of certain graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5:19–27.
MLA Kok, Johan and Saptarshi Bej. “Coloring Sums of Extensions of Certain Graphs”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 5, no. 1, 2018, pp. 19-27, doi:10.13069/jacodesmath.349383.
Vancouver Kok J, Bej S. Coloring sums of extensions of certain graphs. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5(1):19-27.