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

$$\begin{aligned} NT(G)= \sum (n(x)-n(y))^2 \ \ \ \forall x,y \in V(G) \end{aligned}$$

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.