Total Domination Type Invariants of Regular Dendrimer

Yıl 2020, Cilt: 16 Sayı: 2, 225 - 228, 24.06.2020

Bünyamin Şahin , Ümmügülsüm Şener

Öz

In this paper total vertex-edge domination number and total edge-vertex domination number are calculated for regular dendrimers. New equations are obtained for regular dendrimers by using geometric series properties.

Anahtar Kelimeler

total domination, total vertex-edge domination, total edge-vertex domination

Kaynakça

• [1]. Haynes, TW, Hedetniemi, ST, Slater, PJ, Fundamentals of Domination in Graphs, Marcel-Dekker, New York, 1998.
• [2]. Haynes, TW, Hedetniemi, ST, Slater, PJ (edts), Fundamentals of Domination in Graphs: Advanced Topics, Marcel-Dekker, New York, 1998.
• [3]. Lewis, JR, Hedetniemi, ST, Haynes, TW, Fricke, GH 2010. Vertex-edge domination. Utilitas Mathematica ;81: 193–213.
• [4]. Boutrig, R, Chellali, M, Haynes, TW, Hedetniemi, ST. 2016. Vertex-edge domination in graphs. Aequationes Mathematica; 90 (2): 355-366.
• [5]. Peters, JW, Theoretical and algorithmic results on domination and connectivity, Ph.D. thesis, Clemson University, 1986.
• [6]. Ediz, S. 2017. A new tool for QSPR researches: ev-degree Randic index, Celal Bayar University Journal of Science; 13 (3): 615-618.
• [7]. Boutrig, R, Chellali, M. 2018. Total vertex-edge domination. International Journal Computer Mathematics; 95 (9): 1820-1828. [8]. Şahin, A, Şahin, B 2020. Total edge-vertex domination. RAIRO Theoretical Informatic and Applications, 54 (1), 1-7.
• [9]. Majstorovic, S, Doslic, T, Klobucar, A. 2012. K-domination on hexagonal cactus chains. Kragujevac Journal of Mathematics; 2: 335-347.
• [10]. Gao,Y, Zhu, E, Shao, Z, Gutman, Klobucar, A. 2018. Total domination and open packing in some chemical graphs. Journal of Mathematical Chemistry ;56: 1481-1492.
• [11]. Hutchinson, L, Kamat,V, Larson, CE, Mehta, S, Muncy, D, Van Cleemput, N. 2018. Automated Conjecturing VI: Domination number of benzenoids. MATCH Communications in Mathematics and Computer Chemistry; 80: 821-834.
• [12]. Quadras, J, Mahiz, ASM, Rajasingh, I, Rajan RS. 2015. Domination in certain chemical graphs. Journal of Mathematical Chemistry; 53: 207–219.
• [13]. Vukicevic, D, Klobucar A. 2007. k-dominating sets on linear benzenoids and on the infinite hexagonal grid. Croatica Chemica Acta; 80 (2): 187-191.
• [14]. Şahin, B, Şahin, A. 2018. On domination type invariants of regular dendrimer. Journal of Mathematical Nanoscience; 8 (1): 27-31.
• [15]. Şener, Ü, Şahin, B. 2019, Total domination number of regular dendrimer graph. Turkish Journal of Mathematics and Computer Science; 11: 81-84.
• [16]. Haynes, TW, Knisley, D, Seier, E, Zou, Y. 2006. A quantitive analysis of secondary RNA structure using domination based parameters on trees. BMC Bioinformatics; 7: 108.
• [17]. Haynes, TW, Hedetniemi, SM, Hedetniemi, ST, Henning, MA. 2002, Domination in graphs applied to electric power networks. SIAM Journal on Discrete Mathematics; 15 (4): 519-529.
• [18]. Ediz, S, Cancan, M. 2020, On molecular topological properties of alkylating agents based anticancer drug candidates via some ve-degree topological indices. Current Computer-aided Drug Design; 16 (2), 190-195.
• [19]. Newkome, GR, Moorefield CN, Vogtle, F, Dendrimers and Dendrons: Concepts, Syntheses, Applications, Wiley-VCH, verlag GmbH and Co.KGaA, 2002.
• [20]. Nagar, AK, Sriam, S. 2016. On eccentric connectivity index of eccentric graph of regular dendrimer, Mathematics in Computer Science; 10, 229-237.