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

P. Aparna, K. V. Suryanarayana Rao, E. Keshava Reddy

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.


Keywords


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

Full Text:

PDF

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.




DOI: http://dx.doi.org/10.26713%2Fcma.v12i1.1406

Refbacks

  • There are currently no refbacks.


eISSN 0975-8607; pISSN 0976-5905