Analyzing the modified symmetric division deg index: mathematical bounds and chemical relevance

Abstract

The modified symmetric division deg (MSD) index of a graph G is precisely defined as $MSD(G)=\sum\limits_{j\sim k}\sqrt{\frac{1}{2} \left(\frac{d_{j}}{d_{k}}+\frac{d_{k}}{d_{j}}\right)}$, where dj and dk represent the degrees of j and k respectively. In this paper,
we present precise bounds for the modified symmetric division deg index, expressed in the relation to
the minimum and maximum degrees, the order and size of the graph, the number of pendant vertices
and the minimum degree of a non-pendant vertex, the forgotten topological index, the modified
second Zagreb index. We determine the upper bounds for the modified symmetric division deg index
of unicyclic, bicyclic and k-cyclic graphs. Moreover, upon analyzing the modified symmetric division
deg index, we observe its correlation with other well-known indices and its chemical applicability on
the molecular graphs of octane isomers. At the end we find chemical applicability of the modified
symmetric division deg index on benzenoid hydrocarbons and observe that the modified symmetric
division deg index have a very strong correlation with physical properties of benzenoid hydrocarbons.