Independent domination polynomial of binary sequence graphs

In this article, we give the explicit formulae for the independence domination polynomial of graphs generated by binary sequence like chain and threshold graphs. We prove that the independence domination polynomial 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 this very polynomial 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 Enestrom-Kakeya theorem, we prove that the zeros of the independent domination polynomial of threshold graphs lie in the annular region bounded between zero and the largest exponent of the first color class.