Generalized transmission neighbor indices: graph connectivity analysis and its chemical relevance

In this article, we introduce a novel concept called Generalized Transmission Neighbor Indices, building upon established transmission indices. The primary focus is on two variants of these indices, denoted as \(TN^1_{(a,b)}(G)\) and \(TN^2_{(a,b)}(G)\), which offer distinct insights into graph connectivity. The first index, \(TN^1_{(a,b)}(G)\), quantifies the sum of powered vertex neighbor transmissions for connected vertices, while the second, \(TN^2_{(a,b)}(G)\), calculates the product of powered vertex neighbor transmissions among connected vertices. Our investigation delves into the diverse values of parameters a and b, shedding light on the relationships between these indices and established transmission neighbor-based metrics. Bounds have been computed, and we have also explored the chemical relevance (Quantitative Structure–Property Relationship) in the context of linear monocarboxylic acids.