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ACHROMATIC COLORING OF QUADRILATERAL SNAKES

Year 2021, Volume: 2 Issue: 1, 1 - 10, 30.06.2021

Akhlak Mansurı Yashwant Panwar

Abstract

The Main objective of this article is to discuss achromatic coloring and to investigate the achromatic 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 χa(C(Qn)), χa{C(DQn)), χa(C(TQn)), χa{C{kQn)),χa{C(AQn)), χa{C(D(AQn))), χa(C(T(AQn))), χa{C{k(AQn))) respectively.

Keywords

Achromatic coloring Achromatic number Central graph Quadrilateral and alternate quadrilateral snakes.

References

  • [1]. Aparna, K. M., Correya, H. & Manjusha (2018). Achromatic Number of Some Graphs, International Journal of Pure and Applied Mathematics, 18(20), 941- 949.
  • [2]. Agasthi, P. & Parvathi, N. (2018). Some Labeling of Quadrilateral Snake, International Journal of Pure and Applied Mathematics, 119(12), 2975-2992.
  • [3]. Bondy, J. A. & U.S.R. Murty (1976). Graph theory with Applications, London: MacMillan.
  • [4]. Chandel, R. S., Mansuri, A. & Mehta, R. (2014). Study on Achromatic Coloring of Triple Star Graph Families, JP Journal of Mathematical Sciences, 10(1 & 2), 7-16.
  • [5]. Gallian, J. A. (2019). A Dynamic survey of graph labeling, The electronic Journal of Combinatorics.
  • [6]. Gopi, R. (2016). Odd sum labeling of alternative quadrilateral snake, Int. J. EnginSci., Adv. Comput. and Bio-Tech., 7(3), 73-77.
  • [7]. Harary, F. (2001). Graph Theory, Narosa Publishing House.
  • [8]. Harary, F. & Hedetniemi, S.T. (1970). The achromatic number of a graph, Journal of Combinatorial Theory, (8), 154-161.
  • [9]. Hell, P. & Miller, D. J. (1976). Graph with given Achromatic number, Discrete Mathe- matics, (16), 195-207.
  • [10].Ponraj R. & Narayanan, S. S. (2014). Difference Cordiality of Some Snake Graphs, J. Appl. Math. & Informatics, 32(3-4), 377-387.
  • [11]. Ponraj R. & Narayanan, S. S. (2013). Difference Cordiality of Some Snake Graphs obtained from double alternate snake graphs, Global J. Math. Sciences: Theory and Practical, (5), 167-175.
  • [12]. Sandhya, S. S., Merly, E. R. & Shiny, B. (2015). Subdivision of super geometric mean labeling for quadrilateral snake graphs, Internat. J. Math. Trends Tech., 24(1), 1-16.
  • [13]. Sandhya, S. S., Merly, E. R. & Shiny, B. (2015). Super geometric mean labeling on doublequadrilateral snake graphs, Asian Pacific J. Res., 1(XXI) 128- 135.
  • [14].Thilagavthi, K. Thilagavathy, K.P. & Roopesh, N. (2009). The achromatic colouring of graphs, Discrete Mathematics, (33), 153-156.
  • [15].Vivin, J. V., Venkatachalam , M. & Akbar, M.M.A. (2009). A note on achromatic coloring of star graph families, Filomat, (23), 251-255.

Year 2021, Volume: 2 Issue: 1, 1 - 10, 30.06.2021

Akhlak Mansurı Yashwant Panwar

Abstract

References

  • [1]. Aparna, K. M., Correya, H. & Manjusha (2018). Achromatic Number of Some Graphs, International Journal of Pure and Applied Mathematics, 18(20), 941- 949.
  • [2]. Agasthi, P. & Parvathi, N. (2018). Some Labeling of Quadrilateral Snake, International Journal of Pure and Applied Mathematics, 119(12), 2975-2992.
  • [3]. Bondy, J. A. & U.S.R. Murty (1976). Graph theory with Applications, London: MacMillan.
  • [4]. Chandel, R. S., Mansuri, A. & Mehta, R. (2014). Study on Achromatic Coloring of Triple Star Graph Families, JP Journal of Mathematical Sciences, 10(1 & 2), 7-16.
  • [5]. Gallian, J. A. (2019). A Dynamic survey of graph labeling, The electronic Journal of Combinatorics.
  • [6]. Gopi, R. (2016). Odd sum labeling of alternative quadrilateral snake, Int. J. EnginSci., Adv. Comput. and Bio-Tech., 7(3), 73-77.
  • [7]. Harary, F. (2001). Graph Theory, Narosa Publishing House.
  • [8]. Harary, F. & Hedetniemi, S.T. (1970). The achromatic number of a graph, Journal of Combinatorial Theory, (8), 154-161.
  • [9]. Hell, P. & Miller, D. J. (1976). Graph with given Achromatic number, Discrete Mathe- matics, (16), 195-207.
  • [10].Ponraj R. & Narayanan, S. S. (2014). Difference Cordiality of Some Snake Graphs, J. Appl. Math. & Informatics, 32(3-4), 377-387.
  • [11]. Ponraj R. & Narayanan, S. S. (2013). Difference Cordiality of Some Snake Graphs obtained from double alternate snake graphs, Global J. Math. Sciences: Theory and Practical, (5), 167-175.
  • [12]. Sandhya, S. S., Merly, E. R. & Shiny, B. (2015). Subdivision of super geometric mean labeling for quadrilateral snake graphs, Internat. J. Math. Trends Tech., 24(1), 1-16.
  • [13]. Sandhya, S. S., Merly, E. R. & Shiny, B. (2015). Super geometric mean labeling on doublequadrilateral snake graphs, Asian Pacific J. Res., 1(XXI) 128- 135.
  • [14].Thilagavthi, K. Thilagavathy, K.P. & Roopesh, N. (2009). The achromatic colouring of graphs, Discrete Mathematics, (33), 153-156.
  • [15].Vivin, J. V., Venkatachalam , M. & Akbar, M.M.A. (2009). A note on achromatic coloring of star graph families, Filomat, (23), 251-255.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research & Review Articles
Authors

Akhlak Mansurı

Yashwant Panwar

Publication Date June 30, 2021
Published in Issue Year 2021 Volume: 2 Issue: 1

Cite

APA Mansurı, A., & Panwar, Y. (2021). ACHROMATIC COLORING OF QUADRILATERAL SNAKES. Journal of Amasya University the Institute of Sciences and Technology, 2(1), 1-10.
AMA Mansurı A, Panwar Y. ACHROMATIC COLORING OF QUADRILATERAL SNAKES. J. Amasya Univ. Inst. Sci. Technol. June 2021;2(1):1-10.
Chicago Mansurı, Akhlak, and Yashwant Panwar. “ACHROMATIC COLORING OF QUADRILATERAL SNAKES”. Journal of Amasya University the Institute of Sciences and Technology 2, no. 1 (June 2021): 1-10.
EndNote Mansurı A, Panwar Y (June 1, 2021) ACHROMATIC COLORING OF QUADRILATERAL SNAKES. Journal of Amasya University the Institute of Sciences and Technology 2 1 1–10.
IEEE A. Mansurı and Y. Panwar, “ACHROMATIC COLORING OF QUADRILATERAL SNAKES”, J. Amasya Univ. Inst. Sci. Technol., vol. 2, no. 1, pp. 1–10, 2021.
ISNAD Mansurı, Akhlak - Panwar, Yashwant. “ACHROMATIC COLORING OF QUADRILATERAL SNAKES”. Journal of Amasya University the Institute of Sciences and Technology 2/1 (June 2021), 1-10.
JAMA Mansurı A, Panwar Y. ACHROMATIC COLORING OF QUADRILATERAL SNAKES. J. Amasya Univ. Inst. Sci. Technol. 2021;2:1–10.
MLA Mansurı, Akhlak and Yashwant Panwar. “ACHROMATIC COLORING OF QUADRILATERAL SNAKES”. Journal of Amasya University the Institute of Sciences and Technology, vol. 2, no. 1, 2021, pp. 1-10.
Vancouver Mansurı A, Panwar Y. ACHROMATIC COLORING OF QUADRILATERAL SNAKES. J. Amasya Univ. Inst. Sci. Technol. 2021;2(1):1-10.



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