For graphs G and H, an H-coloring of G is a map from the vertices of G to the vertices of H that preserves edge adjacency. We consider the following extremal enumerative question: for a given H, which connected n-vertex graph with minimum degree δ maximizes the number of H-colorings? We show that for non-regular H and sufficiently large n, the complete bipartite graph Kδ,n−δ is the unique maxim...

The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...

Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the generation of unlabeled graph up to an isomorphism. In this paper, we present the full development of a generation engine by describing the related theory, establishing a mathematical and practical complexity, and exposin...

1. Introduction. The Lagrange inversion formula is one of the fundamental results of enumerative combinatorics. It expresses the coefficients of powers of the compositional inverse of a power series in terms of the coefficients of powers of the original power series. G. Labelle [10] extended Lagrange inversion to cycle index series, which are equivalent to symmetric functions. Although motivate...