DOMINATION POLYNOMIALS OF SOME NOTABLEGRAPH FAMILIES

Abstract

A graph polynomial is a graph invariant that evaluates to a
polynomial expression. The study of graph polynomials, including their definition and determination, constitutes a fundamental area of research in graph theory. Among these, the domination polynomial stands out, providing valuable insights into the structural properties of a graph. This research contributes to the advancement of domination theory—a branch of graph theory with broad applications—by deriving explicit expressions  for the domination polynomials of some significant graphs, namely the
path graph Pn, the star graph Sn, the centipede graph CPn, and the
corona of the graphs Pn and mK1. The study employs a streamlined and unified methodology based on simultaneous recurrence relations and matrix diagonalisation.