Abstract:
The concept of the Wiener distance is considered one of the fundamental pillars in chemical graph theory, having served over the past decades as the foundation from which numerous distance-based measures-and consequently, various topological indices-have emerged. These indices are widely used in analyzing and predicting the physical properties of a wide range of chemical compounds.
Among these concepts is the restricted detour distance, defined as the length of the longest induced path between two vertices and in a connected graph , such that the set of vertices P forming this path induced a subgraph of i.e., . The corresponding restricted detour index is defined as the sum of the restricted detour distance over all unordered pairs of distinct in the graph .
This paper presents a historical review of the concept of restricted detour distance, its associated index, and the corresponding polynomial. We also highlight the most significant research papers that have addressed the computation of this index for certain types of graph operations, particularly those that result in straight chain graphs. In addition, we explore a practical application involving the use of the restricted detour index to identify a correlation with the boiling point of a group of hexagonal carbon compounds.
Key words: chain graphs, chemical graphs, graph operations, restricted detour index.
