Unimodality of independence polynomials of the incidence product of graphs

摘要

Given two graphs G and H, assume that V(G) = {v(1) ,v(2), . . . , v(n),} and U is a subset of V(H). We introduce a new graph operation called the incidence product, denoted by G circle dot H-u, as follows: insert a new vertex into each edge of G, then join with edges those pairs of new vertices on adjacent edges of G. Finally, for every vertex v(i) is an element of V(G), replace it by a copy of the graph H and join every new vertex being adjacent to v(i) to every vertex of U. It generalizes the line graph operation. We prove that the independence polynomial