Main Article Content

Abstract

This article shows the study about the harmonious coloring and to investigate the harmonious chromatic number of the central graph of quadrilateral snake, double quadrilateral snake, triple quadrilateral snake, k-quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake, triple alternate quadrilateral snake and k-alternate quadrilateral snake, denoted by C(Qn), C(DQn), C(TQn), C(kQn), C(AQn), C(D(AQn)), C(T(AQn)), C(k(AQn)) respectively.

Keywords

Harmonious coloring Harmonious chromatic number Cen- tral graph Quadrilateral and alternate quadrilateral snakes

Article Details

Author Biographies

Akhlak Mansuri, Government Girls College, Mandsaur (M.P. ) India

Assistant Professor  Department of Mathematics

Rohit Mehta, Radharamn Engineering College, Bhopal

Assistant Professor, Department of Engineering Mathematics

R S Chandel, Government Geetanjali Girls College, Bhopal

Professor, Department of Mathematics
How to Cite
Mansuri, A., Mehta, R., & Chandel, R. S. (2021). Central Graph of Quadrilateral Snakes with Chromatic Number. Journal of the Indonesian Mathematical Society, 27(1), 1–8. https://doi.org/10.22342/jims.27.1.948.1-8

References

  1. Agasthi P., Parvathi N., On Some Labeling of Quadrilateral Snake, International Journal of Pure and Applied Mathematics, 119(12), (2018), 2975-2992.
  2. Bondy J. A. and Murty U.S.R., Graph theory with Applications, London: MacMillan, (1976).
  3. Gallian J. 1 A. , A Dynamic survey of graph labeling, The electronic Journal of Combinatorics,
  4. (2019),#DS6
  5. Gopi R. , Odd sum labeling of alternative quadrilateral snake, Internat. J. EnginSci., Advan. Comput. and Bio-Tech. , 7(3),(2016), 73-77.
  6. Harary F. , Graph Theory, Narosa Publishing home, (1969).
  7. Hopcroft J. and Krishnamoorthy M.S. , On the harmonious coloring of graphs, SIAM J. Algebra Discrete Math, 4, (1983), 306-311.
  8. MansuriA. , On harmonious Chromatic Number of Triple star graph, Journal of Hyperstruc tures, 5(1), (2016), 26-32.
  9. Miller Z. , Pritikin D. : The harmonious coloring number of a graph, Discrete Mathematics, 93, (1991), 211-228.
  10. Ponraj R. and Narayanan S. S., Dierence Cordiality of Some Snake Graphs obtained from double alternate snake graphs, Global J. Math. Sciences: Theory and Practical, (5), (2013),
  11. -175.
  12. Ponraj R. and Narayanan S. S., Dierence Cordiality of Some Snake Graphs, J. Appl. Math.& Informatics, 32(3-4), (2014), 377-387.
  13. Ponraj R. and Narayanan S. S., Dierence Cordiality of Some derived Graphs, J. Math. Combin., (4), (2013), 37-48.
  14. Ponraj R. and Narayanan S. S. and Kala R., Dierence cordial labeling of graphs obtained from double snakes, Internat. J. of Math. Research, (5), (2013), 317-322.
  15. Rathod N. B. and Kanani K. K. , V4-cordial labeling of quadrilateral snakes, Internat. J. Emerging Tech. Appl. Eng., Tech., Sci., (9), (2016), 45-51.
  16. Sandhya S. S. , Ebin Raja Merly E. and Deepa S.D., Heronian Mean Labeling of Triple Triangular and Triple Quadrilateral Snake Graphs, International Journal of Applied Mathematical Sciences , 9(2), (2016), 177-186.
  17. Sandhya S. S. , Raja Merly E. and Shiny B. , Subdivision of super geometric mean labeling for quadrilateral snake graphs, Internat. J. Math. Trends Tech. , 24(1), (2015), 1-16.
  18. Sandhya S. S. , Raja Merly E. and Shiny B. , Super geometric mean labeling on double quadrilateral snake graphs, Asian Pacic J. Res., 1(XXI), (2015), 128-135.
  19. Venkatachalam M. , Vernold Vivin J. and Kaliraj K., Harmonious Coloring On Double Star Graph families, Tamkang Journal of Mathematics, 43(2),(2012), 153-158.
  20. Vernold Vivin J. And Thilagavathi K. , On Harmonious Colouring of Line Graph of Central Graph of Paths , Applied Mathematical Sciences, 3(5),(2009), 205-214.