A Note on Isolate Domination Number of a Cubic Graph

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Authors

  • Shilpa T. Bhangale
     Department of Engineering Sciences, Ramrao Adik Institute of Technology, D. Y. Patil Deemed to be University, Nerul, Navi Mumbai,400706 ,IN
  • Madhukar M. Pawar
     Department of Mathematics, S. S. V. P.S’s. Late Kr. Dr., P. R. Ghogrey Science College, Dhule-424005 ,IN

DOI:

https://doi.org/10.18311/jims/2023/31295

Keywords:

Domination Number, Isolate Domination Number, Total Domination Number, Cubic Graphs, Private Neighbour.

Abstract

In this note we provide a solution to the problem “Find a structural characterization of cubic graph for which the isolate domination number equals one plus its domination number.” We show that if G is a cubic graph of order n and if 6 | n, then the isolate domination number of G is the same as the domination number of G. We also prove that if G is a connected cubic graph with diam(G) > 2, then the isolate domination number is the same as the domination number.

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Published

2023-03-24

How to Cite

Bhangale, S. T., & Pawar, M. M. (2023). A Note on Isolate Domination Number of a Cubic Graph. The Journal of the Indian Mathematical Society, 90(1-2), 67–74. https://doi.org/10.18311/jims/2023/31295

Issue

Volume 90, Issue 1-2, January-June 2023

Section

Articles

License

Copyright (c) 2023 Shilpa T. Bhangale, Madhukar M. Pawar

Creative Commons License

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

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