Let G be a chemical graph with vertex set {v₁, v₁, … , v_n} and degree sequence d(G) = (deg_G(v₁), deg_G(v₂), … , deg_G(v_n)). The inverse degree, R(G) of G is defined as R(G)=∑i=1n1degG(vi). The cyclomatic number of G is defined as γ = 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.

Keywords: diameter, cyclomatic number, pendant vertex, inverse degree, chemical graph