Vertex-degree-based topological indices of uniform directed hypergraphs

Modelling a chemical network is crucial for understanding the complex interactions and dynamics within a chemical system, allowing for precise predictions of reaction behaviour under various conditions. It aids in the identification of key reaction pathways and the optimization of reaction conditions, enhancing efficiency and yield in industrial processes. A topological index is a numerical measure or a descriptor derived from the structural topology of a network. This article explains a directed hypergraph model to depict a chemical reaction. The definition of vertex-degree-based topological indices has been generalized from directed graphs to directed hypergraphs. Let (Formula presented.) and (Formula presented.) respectively, be the number of vertices with out-degree i and in-degree j. For a function f on k variables and for a given set of k-tuples (Formula presented.) if there exists a unique function (Formula presented.) satisfying (Formula presented.) then an expression in terms of (Formula presented.) and (Formula presented.) is found for a vertex-degree based topological index (corresponding to f) of k-uniform directed hypergraphs.