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Total Domination Number of Regular Dendrimer Graph

Yıl 2019, Cilt: 11, 81 - 84, 30.12.2019

Öz

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

Kaynakça

  • 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.
Yıl 2019, Cilt: 11, 81 - 84, 30.12.2019

Öz

Kaynakça

  • 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.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ümmügülsüm Şener 0000-0002-9801-187X

Bünyamin Şahin 0000-0003-1094-5481

Yayımlanma Tarihi 30 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 11

Kaynak Göster

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. Aralık 2019;11:81-84.
Chicago Şener, Ümmügülsüm, ve Bünyamin Şahin. “Total Domination Number of Regular Dendrimer Graph”. Turkish Journal of Mathematics and Computer Science 11, Aralık (Aralık 2019): 81-84.
EndNote Şener Ü, Şahin B (01 Aralık 2019) Total Domination Number of Regular Dendrimer Graph. Turkish Journal of Mathematics and Computer Science 11 81–84.
IEEE Ü. Şener ve B. Şahin, “Total Domination Number of Regular Dendrimer Graph”, TJMCS, c. 11, ss. 81–84, 2019.
ISNAD Şener, Ümmügülsüm - Şahin, Bünyamin. “Total Domination Number of Regular Dendrimer Graph”. Turkish Journal of Mathematics and Computer Science 11 (Aralık 2019), 81-84.
JAMA Şener Ü, Şahin B. Total Domination Number of Regular Dendrimer Graph. TJMCS. 2019;11:81–84.
MLA Şener, Ümmügülsüm ve Bünyamin Şahin. “Total Domination Number of Regular Dendrimer Graph”. Turkish Journal of Mathematics and Computer Science, c. 11, 2019, ss. 81-84.
Vancouver Şener Ü, Şahin B. Total Domination Number of Regular Dendrimer Graph. TJMCS. 2019;11:81-4.