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- Title
REGNANT AND CAPTIVE DOMINATION IN SOME GENERALIZED GRAPHS.
- Authors
Mehra, Arvind; Mehra, Seema
- Abstract
The term "Regnant Domination" is presented in this study as a novel idea in graph dominance. Let D' = V(G). Then D' is an RD-set if all vertices of D' are adjacent to at least a single vertex of V - D' except one, i.e., in the subset D', if exactly one vertex is not adjacent to any of the vertex of V - D', then D' 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.
- Subjects
PETERSEN graphs; DOMINATING set; WINDMILLS
- Publication
Advances & Applications in Discrete Mathematics, 2022, Vol 34, Issue 1, p87
- ISSN
0974-1658
- Publication type
Article
- DOI
10.17654/0974165822045