Exploring Certified Domination Subdivision Numbers in Graph Theory
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.6713Keywords:
Domination number, Certified domination number, Subdivision number, Certified domination subdivision numberAbstract
A certified dominating set S is a dominating set of a graph G, if every vertex in S has either zero or at least two neighbours in V \S. The minimum cardinality of certified dominating set of G is the certified domination number of G denoted by γcer(G). We defined certified domination subdivision number Sd+γcer (G) [Sd−γcer (G)] of a graph G to be the minimum number of edges that
must be subdivided (where no edge in G can be subdivided more than once) in order to construct a graph with a certified domination number larger [lesser] than the certified domination number of G. In this paper, we determine the values of certified domination subdivision number for certain classes of graphs including circulant graphs [Cn(1, 2) and Cn(1, 3)] and petersen graphs [P(n, 1) and P(n, 2)].
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Copyright (c) 2025 Navamani G. , Sumathi N., Mohankumar Dharmaraj, Luminiţa-Ioana Cotîrlă, Daniel Breaz
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