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Authors
Affiliations
1 Department of Engineering Sciences, Ramrao Adik Institute of Technology, D. Y. Patil Deemed to be University, Nerul, Navi Mumbai, 400706, IN
2 Department of Mathematics, S. S. V. P.S’s. Late Kr. Dr., P. R. Ghogrey Science College, Dhule- 424005, IN
Source
The Journal of the Indian Mathematical Society, Vol 90, No 1-2 (2023), Pagination: 67-74
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
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