Abstract
The study of topological indices – graph invariants that can be used for describing and predicting physicochemical or pharmacological properties of organic compounds – is currently one of the most active research fields in chemical graph theory. In this paper we study the Schultz index and find a relation with the Wiener index of the armchair polyhex nanotubes TUV C6[2p; q]. An exact expression for Schultz index of this molecule is also found.
Highlights
Topological indices are a convenient method of translating chemical constitution into numerical values that can be used for correlations with physical, chemical or biological properties
If d(u, v) is the distance of the vertices u and v of the undirected connected graph G and V (G) is the vertex set of G, the Wiener index of G is the half sum of distances over all its vertex pairs (u, v): W (G) =
The Schultz index of the graph G was introduced by Schultz [14] in 1989 and is defined as follows: S(G) =
Summary
Topological indices are a convenient method of translating chemical constitution into numerical values that can be used for correlations with physical, chemical or biological properties. If d(u, v) is the distance of the vertices u and v of the undirected connected graph G (i.e., the number of edges in the shortest path that connects u and v) and V (G) is the vertex set of G, the Wiener index of G is the half sum of distances over all its vertex pairs (u, v): W (G) = The Schultz index of the graph G was introduced by Schultz [14] in 1989 and is defined as follows: S(G) = A comparative study of molecular descriptors showed that the Schultz index and Wiener index are mutually related [16,17,18].
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