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Total Domination Number of Regular Dendrimer Graph

Year 2019, Volume: 11, 81 - 84, 30.12.2019

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

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 Articles
Authors

Ümmügülsüm Şener 0000-0002-9801-187X

Bünyamin Şahin 0000-0003-1094-5481

Publication Date December 30, 2019
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.
AMA Şener Ü, Şahin B. Total Domination Number of Regular Dendrimer Graph. TJMCS. December 2019;11:81-84.
Chicago Şener, Ümmügülsüm, and Bünyamin Şahin. “Total Domination Number of Regular Dendrimer Graph”. Turkish Journal of Mathematics and Computer Science 11, December (December 2019): 81-84.
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 Ü. Şener and B. Şahin, “Total Domination Number of Regular Dendrimer Graph”, TJMCS, vol. 11, pp. 81–84, 2019.
ISNAD Şener, Ümmügülsüm - Şahin, Bünyamin. “Total Domination Number of Regular Dendrimer Graph”. Turkish Journal of Mathematics and Computer Science 11 (December 2019), 81-84.
JAMA 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, 2019, pp. 81-84.
Vancouver Şener Ü, Şahin B. Total Domination Number of Regular Dendrimer Graph. TJMCS. 2019;11:81-4.