The Forcing Geodetic Cototal Domination Number of a Graph

Authors

  • S L Sumi Research Scholar, Register No.20123042092007, Department of Mathematics,Holy Cross College (Autonomous), Nagercoil - 629004, Affiliated by Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012, Tamil Nadu, India
  • V Mary Gleeta Assistant Professor, Department of Mathematics, T.D.M.N.S College, T. Kallikulam - 627 113, Affiliated by Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012, Tamil Nadu.
  • J Befija Minnie Assistant Professor, Department of Mathematics, Holy Cross College (Autonomous), Nagercoil - 629004, Affiliated by Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012,

DOI:

https://doi.org/10.23755/rm.v44i0.895

Keywords:

geodetic set, cototal dominating set, geodetic cototal dominating set, geodetic cototal domination number, forcing geodeticcototal domination number.

Abstract

Let  be a geodetic cototal domination set of . A subset  is called a forcing subset for  if  is the unique minimum geodetic cototal domination set containing . The minimum cardinality T is the forcing geodetic cototal domination number of S is denotedby , is the cardinality of a minimum forcing subset of S. The forcing geodetic cototal domination number of ,denoted by , is , where the minimum is takenover all -sets  in . Some general properties satisfied by this concept arestudied. It is shown that for every pair  of integers with ,there exists a connected graph  such that  and . where  isthe geodetic cototal dominating number of .

References

F.Harary, Graph Theory, Addison – Wesley, (1969).

F. Buckley and F.Harary,Distance in Graphs, Addition-Wesley,Redwood City,CA,(1990).

T.W.Haynes, S.T.Hedetniemi and P.J.Slater, Fundamentals of domination in graphs, Marcel Dekker, New York, 1998.

V.R. Kulli, B.Janakiram and Radha RajamaniIyer, The cototal dominationnumber of a graph, Journal of Discrete Mathematical Sciences and Cryptography,2 (2), (1999), 179 – 184.

Gary Chartrand and P. Zhang, The Forcing Geodetic number of a Graph,DiscussionesMathematicae Graph Theory 19(1999), 45 – 58.

S.L.Sumi,V.MaryGleeta and J.Befija Minnie, The Geodetic cototal domination Number of a graph, ICDM 2021, ISBN:978-93-91077-53-2.

Downloads

Published

2022-12-11

Issue

Vol. 44 (2022): Special Issue: Recent Trends in Mathematics and its Applications

Section

Volume 45-2023

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.