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Year 2019, Volume: 68 Issue: 2, 1265 - 1272, 01.08.2019
https://doi.org/10.31801/cfsuasmas.517878

Abstract

References

  • Bondy, J.A.and Murty, U.S.R., Graph theory with applications, London : MacMillan, 1976.
  • West, Douglas B., Introduction to graph theory, Second edition, Prentice-Hall of India Private Limited, New Delhi, 2006.
  • Harary, Frank, Hedetniemi, Stephen and Prins, Geert, An interpolation theorem for graphical Homomorphisms, Portugaliae Mathematica, 26-Fasc.4 (1967), 453-462.
  • Jonathan Gross and Jay Yellen, Hand book of Graph theory, CRC Press, New York, 2004.
  • Mohanapriya, N.,Vernold, Vivin J., Venkatachalam, M., On Dynamic coloring of Fan graphs, International Journal of Pure and Applied Mathematics, Volume 106, No. 8 (2016), 169-174.
  • Nithyadevi, N. and Vijayalakshmi, D., On Achromatic Coloring of C(CH_{n}), C(Y_{n}), C(D(T_{n})) and L(K_{m,n}), IAETSD Journal for Advanced Research in Applied Sciences, Volume 5, No. 4 (2018), 222-236.
  • Hell, Pavol and Miller, D.J,.Graphs with given achromatic number, Discrete Mathematics, 16(1976), 195-207.
  • Thilagavathi, K., Thilagavathy, K.P. and Roopesh, N., The achromatic coloring of graphs, Electronic Notes in Discrete Mathematics, 33(2009), 153-156.
  • Thilagavathi, K. and Roopesh, N., Generalization of achromatic coloring of Central graphs, Electronic Notes in Discrete Mathematics, 33(2009), 147-152.
  • Thilagavathi, K.,Vijayalakshmi, D.and Roopesh, N., b-Colouring of Central Graphs, International Journal of Computer Applications, (2010) volume 3-No.11.
  • Vernold, Vivin J., Venkatachalam, M. and Akbar, Ali M.M., A note on achromatic coloring of Star graph families, Faculty of Sciences and Mathematics, University of Niŝ, Serbia, Filomat 23:3(2009), 251-255.
  • Vivin, J. Vernold, Harmonious Coloring of Total Graphs, n-leaf, Central Graphs and Circumdetic Geraphs, Ph.D Thesis, Bharathiar University, India, 2007.
  • Yannakakis, M. and Gavril, F., Edge dominating sets in graphs, SIAM Journal of Applied Mathematics, 38(1980), 364-372.

On achromatic number of central graph of some graphs

Year 2019, Volume: 68 Issue: 2, 1265 - 1272, 01.08.2019
https://doi.org/10.31801/cfsuasmas.517878

Abstract

The concept of coloring a graph will lead to the definition of a complete n- coloring of a graph G which results the achromatic number ψ(G) where the maximum number of colors required for the points of G in which every pair of colors appears on at least one pair of adjacent vertices. In this paper, we obtain the achromatic number for the Central graph of Ladder graph, Central graph of Dutch-Windmill graph, Central graph of Fan graph and Central graph of Flower graph is denoted as ψ[C(L_{n})], ψ[C(D₃⁽ⁿ⁾)], ψ[C(F_{m,n})] and ψ[C(FL_{n})] respectively.

References

  • Bondy, J.A.and Murty, U.S.R., Graph theory with applications, London : MacMillan, 1976.
  • West, Douglas B., Introduction to graph theory, Second edition, Prentice-Hall of India Private Limited, New Delhi, 2006.
  • Harary, Frank, Hedetniemi, Stephen and Prins, Geert, An interpolation theorem for graphical Homomorphisms, Portugaliae Mathematica, 26-Fasc.4 (1967), 453-462.
  • Jonathan Gross and Jay Yellen, Hand book of Graph theory, CRC Press, New York, 2004.
  • Mohanapriya, N.,Vernold, Vivin J., Venkatachalam, M., On Dynamic coloring of Fan graphs, International Journal of Pure and Applied Mathematics, Volume 106, No. 8 (2016), 169-174.
  • Nithyadevi, N. and Vijayalakshmi, D., On Achromatic Coloring of C(CH_{n}), C(Y_{n}), C(D(T_{n})) and L(K_{m,n}), IAETSD Journal for Advanced Research in Applied Sciences, Volume 5, No. 4 (2018), 222-236.
  • Hell, Pavol and Miller, D.J,.Graphs with given achromatic number, Discrete Mathematics, 16(1976), 195-207.
  • Thilagavathi, K., Thilagavathy, K.P. and Roopesh, N., The achromatic coloring of graphs, Electronic Notes in Discrete Mathematics, 33(2009), 153-156.
  • Thilagavathi, K. and Roopesh, N., Generalization of achromatic coloring of Central graphs, Electronic Notes in Discrete Mathematics, 33(2009), 147-152.
  • Thilagavathi, K.,Vijayalakshmi, D.and Roopesh, N., b-Colouring of Central Graphs, International Journal of Computer Applications, (2010) volume 3-No.11.
  • Vernold, Vivin J., Venkatachalam, M. and Akbar, Ali M.M., A note on achromatic coloring of Star graph families, Faculty of Sciences and Mathematics, University of Niŝ, Serbia, Filomat 23:3(2009), 251-255.
  • Vivin, J. Vernold, Harmonious Coloring of Total Graphs, n-leaf, Central Graphs and Circumdetic Geraphs, Ph.D Thesis, Bharathiar University, India, 2007.
  • Yannakakis, M. and Gavril, F., Edge dominating sets in graphs, SIAM Journal of Applied Mathematics, 38(1980), 364-372.
There are 13 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

N. Nithyadevi This is me 0000-0002-9677-7281

D. Vijayalakshmi This is me 0000-0002-8925-1134

Publication Date August 1, 2019
Submission Date February 5, 2018
Acceptance Date May 16, 2018
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Nithyadevi, N., & Vijayalakshmi, D. (2019). On achromatic number of central graph of some graphs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1265-1272. https://doi.org/10.31801/cfsuasmas.517878
AMA Nithyadevi N, Vijayalakshmi D. On achromatic number of central graph of some graphs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1265-1272. doi:10.31801/cfsuasmas.517878
Chicago Nithyadevi, N., and D. Vijayalakshmi. “On Achromatic Number of Central Graph of Some Graphs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1265-72. https://doi.org/10.31801/cfsuasmas.517878.
EndNote Nithyadevi N, Vijayalakshmi D (August 1, 2019) On achromatic number of central graph of some graphs. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1265–1272.
IEEE N. Nithyadevi and D. Vijayalakshmi, “On achromatic number of central graph of some graphs”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1265–1272, 2019, doi: 10.31801/cfsuasmas.517878.
ISNAD Nithyadevi, N. - Vijayalakshmi, D. “On Achromatic Number of Central Graph of Some Graphs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1265-1272. https://doi.org/10.31801/cfsuasmas.517878.
JAMA Nithyadevi N, Vijayalakshmi D. On achromatic number of central graph of some graphs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1265–1272.
MLA Nithyadevi, N. and D. Vijayalakshmi. “On Achromatic Number of Central Graph of Some Graphs”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1265-72, doi:10.31801/cfsuasmas.517878.
Vancouver Nithyadevi N, Vijayalakshmi D. On achromatic number of central graph of some graphs. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1265-72.

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

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