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

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 AZI and ABC for transformed families of graphs Γnk,l and AαΓnk,l. We investigated the fact of pendent paths and the transformation Aα 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.