TY  - JOUR
T1  - Total Domination Number of Regular Dendrimer Graph
AU  - Şahin, Bünyamin
AU  - Şener, Ümmügülsüm
PY  - 2019
DA  - December
JF  - Turkish Journal of Mathematics and Computer Science
JO  - TJMCS
PB  - Matematikçiler Derneği
WT  - DergiPark
SN  - 2148-1830
SP  - 81
EP  - 84
VL  - 11
LA  - en
AB  - In this paper total domination number is calculated for regular dendrimer graph. New equations are obtained for regular dendrimers by using geometric series properties.
KW  - domination
KW  - total domination
CR  - 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.
CR  - Haynes, T.W., Hedetniemi, S.T., Slater, P.J., Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
CR  - Haynes, T.W., Hedetniemi, S.T., Slater, P.J. (eds), Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998.
CR  - 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.
CR  - Majstorovic, S., Doslic, T., Klobucar, A., {\em k-domination on hexagonal cactus chains},Kragujevac Journal of Mathematics, \textbf{2}(2012), 335--347.
CR  - 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.
CR  - Newkome, G.R., Moorefield, C.N., Vogtle, F., Dendrimers and Dendrons: Concepts, Syntheses, Applications, Wiley-VCH, verlag GmbH and Co.KGaA, 2002.
CR  - 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.
CR  - \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.
CR  - 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.
UR  - https://dergipark.org.tr/en/pub/tjmcs/issue//612780
L1  - https://dergipark.org.tr/en/download/article-file/913501
ER  -