Atom bond connectivity index for graph with self-loops and its application to structure property relationships in anticancer drugs

Document Type

Article

Publication Title

Scientific Reports

Abstract

Let be a graph derived from a simple graph G by adding a self-loop to each vertex in a subset. In this paper, we define the atom bond connectivity index of the graph as and the atom bond connectivity energy of as. We obtained upper bounds for the ABC spectral radius of the graph as well as bounds for and in terms of m, n, and. Additionally, we computed the ABC energy for complete graph, cocktail party graph and crown graph with self-loops. We also derived the characteristic polynomial of double star graph with self-loops. Furthermore, we explored the correlation between and various physico-chemical properties, such as boiling point (BP) and molar refraction (MR). Furthermore, we established correlations between and specific indices, specifically the Sombor index of a graph, first Zagreb index of a graph, and Randic index of a graph.

DOI

10.1038/s41598-025-09789-z

Publication Date

12-1-2025

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