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Total Domination Number of Regular Dendrimer Graph

Year 2019, Volume: 11, 81 - 84, 30.12.2019
https://izlik.org/JA52LG39WK

Abstract

In this paper total domination number is calculated for regular dendrimer graph. New equations are obtained for regular dendrimers by using geometric series properties.

References

  • Gao, Y., Zhu, E., Shao, Z., Gutman, I., Klobucar, A., {\em Total domination and open packing in some chemical graphs}, Journal of Mathematical Chemistry, \textbf{56}(2018), 1481--1492.
  • Haynes, T.W., Hedetniemi, S.T., Slater, P.J., Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
  • Haynes, T.W., Hedetniemi, S.T., Slater, P.J. (eds), Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998.
  • Hutchinson, L., Kamat, V., Larson, C.E., Mehta, S., Muncy, D., Van Cleemput, N., {\em Automated Conjecturing VI: Domination number of benzenoids}, MATCH Commun. Math. Comput. Chem., \textbf{80}(2018), 821--834.
  • Majstorovic, S., Doslic, T., Klobucar, A., {\em k-domination on hexagonal cactus chains},Kragujevac Journal of Mathematics, \textbf{2}(2012), 335--347.
  • Nagar, A.K., Sriam, S., {\em On eccentric connectivity index of eccentric graph of regular dendrimer}, Mathematics in Computer Science, \textbf{10}(2016), 229--237.
  • Newkome, G.R., Moorefield, C.N., Vogtle, F., Dendrimers and Dendrons: Concepts, Syntheses, Applications, Wiley-VCH, verlag GmbH and Co.KGaA, 2002.
  • Quadras, J., Mahizl, A.S.M., Rajasingh, I., Rajan, R.S., {\em Domination in certain chemical graphs}, J. Mathematical Chemistry, \textbf{53}(2015), 207--219.
  • \c{S}ahin, B., \c{S}ahin, A., {\em On domination type invariants of regular dendrimer}, Journal of Mathematical Nanoscience, \textbf{8(1)}(2018), 27--31.
  • Vukicevic, D., Klobucar, A., {\em k-dominating sets on linear benzenoids and on the infinite hexagonal grid}, Croatica Chemica Acta, \textbf{80(2)}(2007), 187--191.

Year 2019, Volume: 11, 81 - 84, 30.12.2019
https://izlik.org/JA52LG39WK

Abstract

References

  • Gao, Y., Zhu, E., Shao, Z., Gutman, I., Klobucar, A., {\em Total domination and open packing in some chemical graphs}, Journal of Mathematical Chemistry, \textbf{56}(2018), 1481--1492.
  • Haynes, T.W., Hedetniemi, S.T., Slater, P.J., Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
  • Haynes, T.W., Hedetniemi, S.T., Slater, P.J. (eds), Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998.
  • Hutchinson, L., Kamat, V., Larson, C.E., Mehta, S., Muncy, D., Van Cleemput, N., {\em Automated Conjecturing VI: Domination number of benzenoids}, MATCH Commun. Math. Comput. Chem., \textbf{80}(2018), 821--834.
  • Majstorovic, S., Doslic, T., Klobucar, A., {\em k-domination on hexagonal cactus chains},Kragujevac Journal of Mathematics, \textbf{2}(2012), 335--347.
  • Nagar, A.K., Sriam, S., {\em On eccentric connectivity index of eccentric graph of regular dendrimer}, Mathematics in Computer Science, \textbf{10}(2016), 229--237.
  • Newkome, G.R., Moorefield, C.N., Vogtle, F., Dendrimers and Dendrons: Concepts, Syntheses, Applications, Wiley-VCH, verlag GmbH and Co.KGaA, 2002.
  • Quadras, J., Mahizl, A.S.M., Rajasingh, I., Rajan, R.S., {\em Domination in certain chemical graphs}, J. Mathematical Chemistry, \textbf{53}(2015), 207--219.
  • \c{S}ahin, B., \c{S}ahin, A., {\em On domination type invariants of regular dendrimer}, Journal of Mathematical Nanoscience, \textbf{8(1)}(2018), 27--31.
  • Vukicevic, D., Klobucar, A., {\em k-dominating sets on linear benzenoids and on the infinite hexagonal grid}, Croatica Chemica Acta, \textbf{80(2)}(2007), 187--191.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Conference Paper
Authors

Ümmügülsüm Şener 0000-0002-9801-187X

Bünyamin Şahin 0000-0003-1094-5481

Publication Date December 30, 2019
IZ https://izlik.org/JA52LG39WK
Published in Issue Year 2019 Volume: 11

Cite

APA Şener, Ü., & Şahin, B. (2019). Total Domination Number of Regular Dendrimer Graph. Turkish Journal of Mathematics and Computer Science, 11, 81-84. https://izlik.org/JA52LG39WK
AMA 1.Şener Ü, Şahin B. Total Domination Number of Regular Dendrimer Graph. TJMCS. 2019;11:81-84. https://izlik.org/JA52LG39WK
Chicago Şener, Ümmügülsüm, and Bünyamin Şahin. 2019. “Total Domination Number of Regular Dendrimer Graph”. Turkish Journal of Mathematics and Computer Science 11 (December): 81-84. https://izlik.org/JA52LG39WK.
EndNote Şener Ü, Şahin B (December 1, 2019) Total Domination Number of Regular Dendrimer Graph. Turkish Journal of Mathematics and Computer Science 11 81–84.
IEEE [1]Ü. Şener and B. Şahin, “Total Domination Number of Regular Dendrimer Graph”, TJMCS, vol. 11, pp. 81–84, Dec. 2019, [Online]. Available: https://izlik.org/JA52LG39WK
ISNAD Şener, Ümmügülsüm - Şahin, Bünyamin. “Total Domination Number of Regular Dendrimer Graph”. Turkish Journal of Mathematics and Computer Science 11 (December 1, 2019): 81-84. https://izlik.org/JA52LG39WK.
JAMA 1.Şener Ü, Şahin B. Total Domination Number of Regular Dendrimer Graph. TJMCS. 2019;11:81–84.
MLA Şener, Ümmügülsüm, and Bünyamin Şahin. “Total Domination Number of Regular Dendrimer Graph”. Turkish Journal of Mathematics and Computer Science, vol. 11, Dec. 2019, pp. 81-84, https://izlik.org/JA52LG39WK.
Vancouver 1.Şener Ü, Şahin B. Total Domination Number of Regular Dendrimer Graph. TJMCS [Internet]. 2019 Dec. 1;11:81-4. Available from: https://izlik.org/JA52LG39WK