Independent domination polynomials of binary sequence graphs

In this article, we give the explicit formulae for the independence domination polynomials of graphs generated by binary sequences like chain and threshold graphs. We prove that the independence domination polynomials of chain graphs with same exponents in binary string, same exponents in each color classes, exponents as consecutive positive integers in one class and reverse in other class are all log-concave and unimodal. We also discuss the zeros of such polynomials for some classes of chain graphs along with identification of graphs having only real zeros. We prove that large class of threshold graphs satisfy log-concave and unimodal properties. Furthermore, with the application of Eneström-Kakeya theorem, we prove that the zeros of the independent domination polynomials of threshold graphs lie in the annular region bounded between zero and the largest exponent of the first color class.