Upper Bounds of AZI and ABC Index for Transformed Families of Graphs

Abstract

Topological index is a mapping which corresponds underlying graph with a numeric value and invariant up to all the isomorphisms of graph. Our study is based on a partial open question regarding topological indices: for which members of n-vertex graph family, certain index has minimum or maximum value? In this work, we answered the above-mentioned question regarding $\text{AZI}$ and $\text{ABC}$ for transformed families of graphs ${\mathrm{\Gamma }}_n^{k,l}$ and $A_{\alpha }\left({\mathrm{\Gamma }}_n^{k,l}\right)$ . We investigated the fact of pendent paths and the transformation $A_{\alpha }$ over these indices and developed the tight upper bounds regarding these families of graphs. Moreover, we characterized transformed graphs associated with maximum values of these indices.