Perfect domination number of path graph $P_n$ and its Corona product with another path graph $P_{n-1}$
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Abstract
According to the research paper on Perfect Dominating Sets by Marilynn Livingston and Quentin F. Stout[1]they have been constructed the PDSs in families of graphs arising from the interconnected networks of parallel computers also contained perfect domination numbers of trees, dags, series-parallel graphs, meshes, tori, hypercubes, cube connected cycles and de Bruijin graphs and give linear algorithms for determining if a PDS exist, and generate a PDS when one does. They also proved that 2 and 3-dimensional hypercube graph having infinitely many PDSs.In this paper We are trying to apply their concept on path graphs and obtained their perfect domination number we also trying to find a corona product of path graph $P_n$ with path graph $P_{n-1}$ and as a conclusion we give such applications of it.
Keywords:
Dominating set, Minimal dominating set, Minimum dominating setMathematics Subject Classification:
Mathematics- Pages: 118-123
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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