Perfect Domination Polynomial of a Graph

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-4
Year of Publication : 2021
Authors : Nayaka S. R, B. Ashwini, B. Sharada, Puttaswamy
  10.14445/22315373/IJMTT-V67I4P515

MLA

MLA Style: Nayaka S. R, B. Ashwini, B. Sharada, Puttaswamy "Perfect Domination Polynomial of a Graph" International Journal of Mathematics Trends and Technology 67.4 (2021):110-113. 

APA Style: Nayaka S. R, B. Ashwini, B. Sharada, Puttaswamy(2021). Perfect Domination Polynomial of a Graph International Journal of Mathematics Trends and Technology, 110-113.

Abstract
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.

Reference 

[1] S. Alikhani, Y.H. Peng, (2014): Introduction to domination polynomial of a graph, Ars Combin. 114 257-266.
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[4] T.W.Haynes, S.T.Hedetniemi, P.J.Slater (1998) Fundamentals of Domination in Graphs, Marcel Dekker, New York.

Keywords : Domination polynomial, Perfect dominating set, Perfect domination number, Perfect domination polynomial.