Generalized Arithmetic Graphs With Equal and Unequal Powers of Annihilator Domination Number

Authors

  • P. Aparna Department of Mathematics, Jawaharlal Nehru Technological University, Anantapuramu, Andhra Pradesh
  • K. V. Suryanarayana Rao Department of Mathematics, Rajeev Gandhi Memorial College of Engineering and Technology, Nandyal, Andhra Pradesh
  • E. Keshava Reddy Department of Mathematics, Jawaharlal Nehru Technological University, Anantapuramu, Andhra Pradesh

DOI:

https://doi.org/10.26713/cma.v12i1.1406

Keywords:

Split dominance, Array and number of annihilator domination, Arithmetic graphs

Abstract

Current work is carried out in Generalized Arithmetic Graphs to explore the theory of conquest by the Annihilator Dominion Number of Upper bound. Kulli and Janakiram [8] first demonstrated split domination while Suryanarayana Rao and Vangipuram [12] introduced the domination of Annihilator and obtained several interesting results in Arithmetic graphs. There are few significant and important studies on Annihilator's domination being examined in the current paper.

Downloads

Download data is not yet available.

References

T. M. Apostol, Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics, Springer-Verlag, Berlin ” Heidelberg (1980), DOI: 10.1007/978-1-4757-5579-4.

S. Arumugam and A. Thuraiswamy, Total domination in graph, Ars Combinatoria 43 (1996), 89 – 92, http://14.139.186.253/id/eprint/2496.

J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, North-Holland (1976), https://snscourseware.org/snsrcas/files/CW_5d16efa85c2e3/BondyMurtyGTWA-compressed.pdf.

E. J. Cockayne and S. T. Hedetniemi, Towards a theory of domination in graphs, Networks 7 (1977), 247 – 271, DOI: 10.1002/net.3230070305.

E. J. Cockayne, R. W. Dawes and S. T. Hedetniemi, Total domination in graphs, Networks 10 (1980), 211 – 219, DOI: 10.1002/net.3230100304.

F. Harary, Graph Theory, Addison-Wesley, Massachusetts (1969), https://www.worldcat.org/title/graph-theory/oclc/64676.

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Graph Domination, Marcel-Dekkar, Inc., New York (1998), https://www.routledge.com/Fundamentals-of-Dominationin-Graphs/Haynes-Hedetniemi-Slater/p/book/9780824700331.

V. R. Kulli and B. Janakiram, The split domination number of a graph, Graph Theory Notes of New York, New York Academy of Sciences, XXXII (1997), 16 – 19.

R. Laskar and H. B. Walikar, On domination related concepts in graph theory, in: Combinatorics and Graph Theory, Lecture Notes in Mathematics 885 (1981), 308 – 320, Springer, Berlin ” Heidelberg, DOI: 10.1007/BFb0092276.

K. V. S. Rao and V. Sreeenivasan, Split domination in product graphs, I.J. Information Engineering and Electronic Business 4 (2013), 51 – 57, http://www.mecs-press.com/ijieeb/ijieeb-v5-n4/IJIEEB-V5-N4-7.pdf.

K. V. S. Rao and V. Sreeenivasan, The split domination in arithmetic graphs, International Journal of Computer Applications 29(3) (2011), 46 – 49, DOI: 10.1.1.259.652.

K. V. Suryanarayana Rao and Vangipuram, The annihilator domination in some standard graphs and arithmetic graphs, International Journal of Pure and Applied Mathematics 106(8) (2016), 123 – 135, DOI: 10.12732/ijpam.v106i8.16.

N. Vasumathi and S. Vangipuram, Existence of a graph with a given domination parameter, in: Proceedings of the Fourth Ramanujan Symposium on Algebra and its Applications, University of Madras, Madras, 187 – 195 (1995), https://www.academia.edu/33290904/Domination-in-Graph-with-Application.

Downloads

Published

31-03-2021
CITATION

How to Cite

Aparna, P., Suryanarayana Rao, K. V., & Reddy, E. K. (2021). Generalized Arithmetic Graphs With Equal and Unequal Powers of Annihilator Domination Number. Communications in Mathematics and Applications, 12(1), 171–187. https://doi.org/10.26713/cma.v12i1.1406

Issue

Vol. 12 No. 1 (2021)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.