The Journal of the Indian Mathematical Society

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A Note on Isolate Domination Number of a Cubic Graph


Affiliations
1 Department of Engineering Sciences, Ramrao Adik Institute of Technology, D. Y. Patil Deemed to be University, Nerul, Navi Mumbai, 400706, India
2 Department of Mathematics, S. S. V. P.S’s. Late Kr. Dr., P. R. Ghogrey Science College, Dhule- 424005, India
     

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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.

Keywords

Domination Number, Isolate Domination Number, Total Domination Number, Cubic Graphs, Private Neighbour.
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  • 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, India
Madhukar M. Pawar
Department of Mathematics, S. S. V. P.S’s. Late Kr. Dr., P. R. Ghogrey Science College, Dhule- 424005, India

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.

Keywords


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

References