Annals of Wiener Index of a Cycle in the Context of Some Graph Operations

Abstract. The Wiener index is one of the oldest molecular-graph-based structure-descriptors. It was first proposed by American Chemist Harold Wiener in 1947 as an aid to determining the boiling point of paraffin. The study of Wiener index is one of the current areas of research in mathematical chemistry. It also gives good correlations between Wiener index (of molecular graphs) and the physico-chemical properties of the underlying organic compounds. That is, the Wiener index of a molecular graph provides a rough measure of the compactness of the underlying molecule. The Wiener index W(G) of a connected graph G is the sum of the distances between all pairs (ordered) of vertices of G. ∑ , , . In this paper, we give theoretical results for calculating the Wiener index of a cycle in the context of some graph operations. These formulas will pave the way to demonstrate the Wiener index of molecular structures