The Detour Domination and Connected Detour Domination values of a graph

Authors

  • R.V Revathi Research Scholar, Department of Mathematics, St. Jude’s College, Thoothoor - 629 176, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012, Tamil Nadu, India
  • M Antony Department of Mathematics, St. Jude’s College, Thoothoor - 629 176, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012, Tamil Nadu, India

DOI:

https://doi.org/10.23755/rm.v44i0.908

Keywords:

domination number, detour number, detour domination value, connected detour domination value, etc.

Abstract

The number of -sets that  belongs to in G is defined as the detour domination value of indicated by for each vertex . In this article, we examined at the concept of a graph’s detour domination value. The connected detour domination values of a vertex  represented as  , are defined as the number of -sets to which a vertex belongs  to G. Some of the related detour dominating values in graphs’ general characteristics are examined. This concept’s satisfaction of some general properties is investigated. Some common graphs are established.

References

Buckley and F.Harary, Distance in Graph, Addition-Wesly-wood city, CA, (1990).

G. Chartrand, G. Johns and P. Zhang, On the detour number and geodetic number of a graph, Ars combinatoria, 72(2004), 3-15.

G. Chartrand, G. Johns and P. Zhang, The detour number of a graph, Utilitas Mathematica, 64(2003), 97-113.

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

J. John and N. Arianayagam, The detour domination number of a graph, Discrete Mathematics Algorithms and Applications, 09(01), 2017, 17500069.

J. John and N. Arianayagam, The total Detour number of a graph, Journal of Discrete Mathematics Sciences and Cryptography, 17(4), 2014, 337-350.

J. John and V. R. Sunil Kumar, The open detour number of a graph, Discrete Mathematics Algorithms and Applications, 13(01), 2021, 2050088.

A. P. Santhakumaran and S. Athisayanathan, The connected detour number of graphs, J. combin.math.combin.compute;69, (2009), 205-218.

Vijaya Xavier Parthian, and C. Caroline Selvaraj, Connected Detour Domination Number of Some Standard Graphs, Journal of Applied Science and Computations, 5(11), (2018), 486-489.

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.