(untitled) (European Journal of Pure and Applied Mathematics, 2024)
Let G = (V(G),E(G)) be a graph with degree sequence d_1,d_2, …, d_n , where d_1 d_2 … d_n. The polynomial representation of G is given by f_G(x) = _i=1^n x^d_i = _k=1^Δ(G)a_kx^k, where a_k is the number of vertices of G having degree k for each i = 1,2, … n = Δ(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.