An Approach to the Extremal Inverse Degree Index for Families of Graphs with Transformation Effect

Abstract

The inverse degree index is a topological index first appeared as a conjuncture made by computer program Graffiti in 1988. In this work, we use transformations over graphs and characterize the inverse degree index for these transformed families of graphs. We established bonds for different families of $n$ -vertex connected graph with pendent paths of fixed length attached with fully connected vertices under the effect of transformations applied on these paths. Moreover, we computed exact values of the inverse degree index for regular graph specifically unicyclic graph.