Domination Polynomials for Inverse Graphs

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-6
Year of Publication : 2022
Authors : J. Baskar Babujee, Temesgen Engida Yimer
 10.14445/22315373/IJMTT-V68I6P501

How to Cite?

J. Baskar Babujee, Temesgen Engida Yimer, "Domination Polynomials for Inverse Graphs," International Journal of Mathematics Trends and Technology, vol. 68, no. 6, pp. 1-7, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I6P501

Abstract
Let G = (V, E) be a simple undirected graph with order n. The inverse, or complement, of a graph G is denoted by G- and is obtained by filling in all the remaining edges needed to form a complete graph while removing all previously existing edges. Equivalently, V(G) = V(G-) and E(G-) = E(Kn) - E(G) and also | E(G-)| = (n/2) - |E(G)|. A domination polynomial of an inverse graph of G is given as D(G-,x) = Σni=γ(G) d(G-,x)xi, where d(G-,x) is the number of all dominating sets of G- with size i and γ(G-) is the minimum domination number of G-. In this paper, we introduce a generating function called a domination polynomial for inverse dominating sets of cycle, star, wheel graphs, and triangular book graphs. Also, the bounds of the minimum dominating number γ(G) discussed with their corresponding inverse of the minimum dominating number γ(G-).

Keywords : Dominating set, Domination polynomials, Inverse of graph.

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