Independent Index Of Unicyclic Graph

The independent index of a graph G , denoted by i(G), is the number of independent sets in G. The trees of order n with the largest and the smallest independent index and the forest of order n with the largest and the smallest independent index are known. The tree of order n with the second smallest independent index is also known. ([1], [6]) In this paper, We mainly study the unicyclic graph of order n with independent index, The unicyclic graph of order n with the largest and the smallest independent index are know(Theorem 2,Theorem 3).We also determine the unicyclic graph of order n with the second largest independent index (Theorem 4,Theorem 5),and the unicyclic graph of order n with the second smallest independent index(Theorem 6, Theorem 7).