Proof of a Conjecture on Symmetric Division Deg Index of Graphs
Kinkar Chandra Das · match Communications in Mathematical and in Computer Chemistry · 2024
Molecular descriptors play a significant role in the quantitative studies on structure-property and structure-activity relationships.One of the popular degree-based topological index, symmetric division deg (SDD) index is a chemically useful descriptor.The SDD index of a graph G is defined aswhere di is the degree of the vertex vi ∈ V (G).Very recently, Ali et al. [Symmetric division deg index: Extremal results and bounds, MATCH Commun.Math.Comput.Chem.90 (2023) 263-299] mentioned several open problems on symmetric division deg index of graphs.One of them is as follows:Characterize graphs attaining the minimum SDD index over the class of all those n-order connected graphs of minimum degree δ that are not δ-regular.In this paper we completely solved the above problem.