International Journal of Mathematics Trends and Technology
Volume 67 | Issue 4 | Year 2021 | Article Id. IJMTT-V67I4P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I4P515
Graph polynomial is one of the algebraic representation for a graph which relates various graph parameters through algebraic operations. In this paper, we initiate the study of one more algebraic representation of a graph called the perfect domination polynomial. The perfect domination polynomial of a graph G of order n is the polynomial 𝐷𝑝(𝐺,𝑥) having the coefficient of 𝑥𝑖 to be 𝑑𝑝(𝐺,𝑖) which denotes the number of perfect dominating sets of 𝐺 of cardinality 𝑖 and 𝛾𝑝(𝐺) denotes the perfect domination number of 𝐺. We obtain some properties of 𝐷𝑝(𝐺,𝑥) and its coefficients, compute the perfect domination polynomial of some families of standard graphs. Further, we obtain some characterization for some specific graphs.
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Nayaka S. R, B. Ashwini, B. Sharada, Puttaswamy, "Perfect Domination Polynomial of a Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 4, pp. 110-113, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I4P515
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