Is every graph the extremal value of a vertex-degree-based topological index (2019)
Let Gn be the set of graphs with n non-isolated vertices. In this paper we identify vertex–degree–based topological indices over Gn with vectors in R h , the Euclidean space with h = (n−1)n 2 coordinates. In this setting, we give an interpretation of the extremal values of a topological index in terms of angles between vectors in R h . Then we consider the following problem: given a graph G0 ∈ Gn, does there exist a vertex–degree–based topological index that attains its extremal values in G0? The answer is affirmative. In order to do this, we introduce the support of the graph G0, the reference vector, and then construct vectors such that G0 is an extremal value.