Reza Sharafdini

Let $G$ be a chemical graph with vertex set $\{v_1,v_1,\ldots,v_n\}$ and degree sequence $d(G)=(\deg_G(v_1),\deg_G(v_2),\ldots,\deg_G(v_n))$. The inverse degree, $R(G)$ of $G$ is defined as $R(G)=\sum_{i=1}^n\frac{1}{\deg_G(v_i)}$. The cyclomatic number of $G$ is defined as $\gamma = m - n k$, where $m$, $n$ and $k$ are the number of edges, vertices and components of $G$, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree