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 W
λ (G), hyper winner
index WW
λ (G), modified hyper winner index WWW
λ (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).
