The term “Regnant Domination” is presented in this study as a novel idea in graph dominance. Let  Then  is an RD-set if all vertices of  are adjacent to at least a single vertex of  except one, i.e., in the subset  if exactly one vertex is not adjacent to any of the vertex of  then  is called an RD-set. We apply this new notion on helm graph to find regnant domination number for this graph. Further, we obtain some results related to captive domination defined by Al-Harere et al. [1] for some generalized graphs like Jahangir graph, helm graph, windmill graph and Petersen graph.

dominating set, domination number, TD-set, TD-number, CD-set, CD-number, Jahangir graph, windmill graph, Helm graph, generalized Petersen graph, RD-set, RD-number.

Received: July 19, 2022; Accepted: September 26, 2022; Published: October 29, 2022

How to cite this article: Arvind and Seema Mehra, Regnant and captive domination in some generalized graphs, Advances and Applications in Discrete Mathematics 34 (2022), 87-99. http://dx.doi.org/10.17654/0974165822045

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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