Polynomial Representation and Degree Sequence of Graphs Resulting from Some Graph Operations

Let G = (V (G), E (G) ) be a graph with degree sequence d₁, d₂, , dₙ, where d₁ d₂ dₙ. The polynomial representation of G is given by fG (x) = ₈=₁ⁿ x^dᵢ = ₊=₁^ (G) aₖx^k, where aₖ is the number of vertices of G having degree k for each i = 1, 2, n = (G). In this paper, we give the polynomial representation of the complement and line graph of a graph, the shadow graph, complementary prism, edge corona, strong product, symmetric product, and disjunction of two graphs.