A new family of expansive graphs Original Research Article

An affine graph is a pair image where G is a graph and image is an automorphism assigning to each vertex of G one of its neighbors. On one hand, we obtain a structural decomposition of any affine graph image in terms of the orbits of image. On the other hand, we establish a relation between certain colorings of a graph G and the intersection graph of its cliques image. By using the results we construct new examples of expansive graphs. The expansive graphs were introduced by Neumann-Lara in 1981 as a stronger notion of the K-divergent graphs. A graph G is K-divergent if the sequence image tends to infinity with n, where image is defined by image for image. In particular, our constructions show that for any image, the complement of the Cartesian product image, where C is the cycle of length image, is image-divergent.