INDEPENDENCE ROOTS AND INDEPENDENCE FRACTALS OF BOOK GRAPHS

The independence polynomial of a graph G is the polynomial I (G, x) = Sigma i(k)x(k) where ik denote the number of independent sets of cardinality k in G. A root of I (G, x) is called an independence root of G. The independence fractal of G is the set I(G) = Roots(I(G(k), x) -1), where G(k) = G[G[...]], and G[H] is the lexicographic product for two graphs G and H. The n-book graph B-n is the graph obtained by joining n copies of the cycle graph C4 with a common edge. In this paper, we investigate the independence polynomial of book graph and its generalization. Also, we study the independence roots and independence fractals of these kind of graphs.