Distance Based Invariants on Embedded Wheel Graphs

Abstract

This study’s main goal is to investigate and understand the mathematical character istics of topological indices. Graph theory heavily depends on these indices, which are mathematical characteristics that measure the topological attributes of chemical compounds. These indicators have been applied across diverse domains such as drug discovery, property forecasting, molecular categorization, and the design of polymers, among other related fields. Our research specifically concentrates on the computation of distance-based topological indicators, with a particular focus on those derived from the eccentricity of both chemical and non-chemical graphs. Our aim is to explore their correlation with a broad spectrum of physical and chemical properties. We aim to calculate several distance-related topological indicators, like hosoya polynomial H(G, x), winner index W(G), modified winner index Wλ (G), hyper winner index WWλ (G), modified hyper winner index WWWλ (G), schultz index Sc(G) and its modified form S ∗ c(G), schultz polynomial Sc(G, x), modified schultz polynomial S ∗ c(G, x), harary polynomial h(G, x), generalized harary index ht(G), multiplicative winner index π(G), eccentric connectivity index ξ (G) and its polynomial ξ (G, x)