Total Domination Number of Regular Dendrimer Graph
Year 2019,
Volume: 11, 81 - 84, 30.12.2019
Ümmügülsüm Şener
,
Bünyamin Şahin
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
Ümmügülsüm Şener
,
Bünyamin Şahin
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.