On the Trinajstic Descriptor of some graphs

Topological descriptors play a crucial role in various scientific fields, particularly in analyzing the physico-chemical and thermodynamic properties of chemical compounds. Recently, a new topological descriptor, known as the Trinajstić descriptor, has been introduced. For a simple connected graph G, the Trinajstić descriptor is defined as (Formula presented.) Where n(x) is the number of vertices whose distance is lesser to x than y and n(y) is the number of vertices whose distance is lesser to y than x. In this article, we calculate the Trinajstić descriptor for the Kite graph, Fan graph, and Helm graph, expanding its applicability to these graph structures.