2-Metro domination number of slanting ladder graph

Authors

  • Ajith P S Dept of Mathematics, Brindavan College of Engineering, Bangalore
  • G C Basavaraju Dept of Mathematics, Brindavan College of Engineering, Bangalore.
  • Vishu Kumar M Dept of Mathematics, REVA University, Bangalore

Keywords:

dominating set, domination number, metric dimension, metro domination

Abstract

A subset D of the vertex set V of the graph  is said to be a dominating set if every vertex in  is adjacent to at least one vertex in D. The minimum cardinality of the dominating set is called the domination number. The metro domination number is the order of a minimum dominating set which resolves as a metric as a metric set. It is denoted by   in this paper we determine the 2- metro domination number of slanting ladder graphs.

Downloads

Download data is not yet available.

References

C. Berge, Graphs and hyper graphs, North-Holland, Amsterdam,1973

B. Zmazek and J. Zerovnik, “On domination number of graph bundles”, Institute of mathematics, physics and mechanics, 43(2005),pp.1-10.

A. Sugumaran and E. Jayachandran, “Domination number of some graphs”, International Journal of Scentific Development and Reserch, 3(2018),no.11,pp.386-391.

Raghunath P and Sooryanarayana B, “Metro domination number of a graph”, Twentieth annual conference of Ramanujan Mathematics Society, July 25-30(2005) university of Calicut, Calicut.

G C Basavaraju, M Vihukumar and Raghunath, “Metro domination of square of path”, Annals of Pure and Applied mathematics, 14(2017), no.3,pp.539-545.

G CBasavaraju, M Vishukumar and Raghunath, “Metro domination of powers of path”, International Journal of Emerging Technology and Advance Engineering, 8(2018), no.1.

G CBasavaraju, M Vishukumar and Raghunath, “On the metro domination number of Cartesian product of P2X Pn”,International Journal of mathematical archieve,9(2018),no.3,pp.1-2

G CBasavaraju, M Vishukumar and Raghunath, “On the metro domination number of Cartesian product of P2X Pnand CmXCn”, Journal of Engineering and applied sciences, 14(2019), no.1, pp.114-119

G CBasavaraju, M Vishukumar and Raghunath, “On the K-metrodomination number of Cartesian product of P2X Pn”, Journal of Advanced Reserch in Dynamical and Control Systems, 11(2019), no.1, pp.425-431.

LalithaLamani and Yogalaksmi S, “Neighborhood, Locating Dominating and Almost Locating Dominating Set of a Ladder Graph”, International Journal of Mathematics Trends and Technology, 67(2021), no.1, pp.121-128.

G CBasavaraju, M Vishukumar and Raghunath, “Metro Domination of Square Cycle”, International Journal of Mathematics and its applications, 5(2017), no.1-E, pp.641-645

Published

18-10-2022

How to Cite

Ajith, P. S., Basavaraju, G. C., & Vishu, K. M. (2022). 2-Metro domination number of slanting ladder graph. International Journal of Health Sciences, 6(S9), 3756–3760. Retrieved from https://sciencescholar.us/journal/index.php/ijhs/article/view/13455

Issue

Vol. 6 No. S9 (2022)

Section

Peer Review Articles
Copyright & Licensing

Copyright (c) 2022 International journal of health sciences

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Articles published in the International Journal of Health Sciences (IJHS) are available under Creative Commons Attribution Non-Commercial No Derivatives Licence (CC BY-NC-ND 4.0). Authors retain copyright in their work and grant IJHS right of first publication under CC BY-NC-ND 4.0. Users have the right to read, download, copy, distribute, print, search, or link to the full texts of articles in this journal, and to use them for any other lawful purpose.

Articles published in IJHS can be copied, communicated and shared in their published form for non-commercial purposes provided full attribution is given to the author and the 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 acknowledgment of its initial publication in this journal.

This copyright notice applies to articles published in IJHS volumes 4 onwards. Please read about the copyright notices for previous volumes under Journal History.