DOMINATION POLYNOMIALS OF SOME NOTABLE GRAPH FAMILIES

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 P_n, the star graph S_n, the centipede graph CP_n, and the corona of the graphs P_n and mK₁. The study employs a streamlined and unified methodology based on simultaneous recurrence relations and matrix diagonalisation.