On f-Symmetries of the Independence Polynomial

An independent set in a graph is a set of pairwise non-adjacent vertices, and α(G) is the size of a maximum independent set in the graph G. If sk is the number of independent sets of cardinality k in G, then I(G;x) = s0 + s1x+ s2x 2 + ...+ sαx α, α = α (G) , is called the independence polynomial of G (I. Gutman and F. Harary, 1983). If sα−i = f (i) · si holds for every i ∈ {0, 1, ..., ⌊α/2⌋}, then I(G;x) is called f symmetric ( f -palindromic). If f (i) = 1, i ∈ {0, 1, ..., ⌊α/2⌋}, then I(G;x) is called symmetric (palindromic). The corona of the graphs G and H is the graph G ◦H obtained by joining each vertex of G to all the vertices of a copy of H . In this paper we show that ifH is a graph with p vertices, q edges, and α (H) = 2, then I (G ◦H ;x) is f -symmetric, where