The Minimal Molecular Tree for the Exponential Randić Index - Jayanta Bera; Kinkar Chandra Das (Mathematics)
Topological indices are numerical parameters that provide a way to quantify the structural features of molecules using their graph representations. In chemical graph theory, these indices have been effectively employed to predict various physico-chemical properties of molecules. Among these, the Randić index stands out as a classical and widely used molecular descriptor in chemistry and pharmacology. The Randić index <semantics>R(G)</semantics> for a given graph G is defined as <semantics>R(G)=<mstyle displaystyle="true"><munder>∑vivj∈E(G)</munder></mstyle><mspace width="0.166667em"></mspace><mstyle scriptlevel="0" displaystyle="true">1<msqrt>d(vi)<mspace width="0.166667em"></mspace>d(vj)</msqrt></mstyle></semantics>, where <semantics>d(vi)</semantics> represents the degree of vertex <semantics>vi</semantics> and <semantics>E(G)</semantics> is the set of edges in the graph G. Given the Randić index’s strong discrimination ability in describing molecular structures, a variant known as the exponential Randić index was recently introduced. The exponential Randić index <semantics>ER(G)</semantics> for a graph G is defined as <semantics>ER(G)=<mstyle displaystyle="true"><munder>∑vivj∈E(G)</munder></mstyle><mspace width="0.166667em"></mspace>e<mstyle scriptlevel="0" displaystyle="true">1<msqrt>d(vi)<mspace width="0.166667em"></mspace>d(vj)</msqrt></mstyle></semantics>. This paper further explores and fully characterizes the minimal molecular trees in relation to the exponential Randić index. Moreover, the chemical relevance of the exponential Randić index is also investigated.