On R Degrees of Vertices and R Indices of Graphs

TL;DR

This paper introduces a new R degree concept for vertices in graphs and defines R indices based on this, providing calculations for common graph types to enhance topological analysis.

Contribution

It proposes a novel R degree concept and corresponding R indices, expanding the tools for graph analysis in chemical and biological modeling.

Findings

R indices computed for paths, stars, complete graphs, and cycles

The R degree concept generalizes classical degree measures

Potential applications in QSAR and QSPR studies

Abstract

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: R degree. And also we define R indices of a simple connected graph by using the R degree concept. We compute the R indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles