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Total Domination Type Invariants of Regular Dendrimer

Year 2020, Volume: 16 Issue: 2, 225 - 228, 24.06.2020

Abstract

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.

References

  • [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.
Year 2020, Volume: 16 Issue: 2, 225 - 228, 24.06.2020

Abstract

References

  • [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.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Bünyamin Şahin

Ümmügülsüm Şener

Publication Date June 24, 2020
Published in Issue Year 2020 Volume: 16 Issue: 2

Cite

APA Şahin, B., & Şener, Ü. (2020). Total Domination Type Invariants of Regular Dendrimer. Celal Bayar University Journal of Science, 16(2), 225-228.
AMA Şahin B, Şener Ü. Total Domination Type Invariants of Regular Dendrimer. CBUJOS. June 2020;16(2):225-228.
Chicago Şahin, Bünyamin, and Ümmügülsüm Şener. “Total Domination Type Invariants of Regular Dendrimer”. Celal Bayar University Journal of Science 16, no. 2 (June 2020): 225-28.
EndNote Şahin B, Şener Ü (June 1, 2020) Total Domination Type Invariants of Regular Dendrimer. Celal Bayar University Journal of Science 16 2 225–228.
IEEE B. Şahin and Ü. Şener, “Total Domination Type Invariants of Regular Dendrimer”, CBUJOS, vol. 16, no. 2, pp. 225–228, 2020.
ISNAD Şahin, Bünyamin - Şener, Ümmügülsüm. “Total Domination Type Invariants of Regular Dendrimer”. Celal Bayar University Journal of Science 16/2 (June 2020), 225-228.
JAMA Şahin B, Şener Ü. Total Domination Type Invariants of Regular Dendrimer. CBUJOS. 2020;16:225–228.
MLA Şahin, Bünyamin and Ümmügülsüm Şener. “Total Domination Type Invariants of Regular Dendrimer”. Celal Bayar University Journal of Science, vol. 16, no. 2, 2020, pp. 225-8.
Vancouver Şahin B, Şener Ü. Total Domination Type Invariants of Regular Dendrimer. CBUJOS. 2020;16(2):225-8.