The Chemical Trees with Minimum Inverse Symmetric Division Deg Index

Abstract:

      Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The inverse symmetric division deg index of $G$ is defined as $ISDD(G)=\sum_{uv \in E(G)}\dfrac{d_ud_v}{d_u^2+d_v^2}$, where $d_u$ and $d_v$ are the degrees of $u$ and $v$, respectively. A tree $T$ is a chemical tree if $d_u\le 4$ for each vertex $u\in V(T)$. In this paper, we characterize the structure of chemical trees with minimum inverse symmetric division deg index among all chemical trees of order $n$.