Abstract

F-index of a graph is the sum of the cube of the degrees of the vertices. Thus, for a graph G with vertex set V(G) and edge set E(G), the degree based topological index F-index is defined as $$F(G)=\sum\limits_{v\in V(G)}{{{d}_{G}}{{(v)}^{3}}}=\sum\limits_{uv\in E(G)}{[{{d}_{G}}{{(u)}^{2}}+{{d}_{G}}{{(v)}^{2}}]},$$ where dG(v) denotes the degree of the vertex v. In this paper, we investigate the F-indices of unicyclic graphs by introducing some transformation, and characterize the unicyclic graphs with the first five largest F-indices and the unicyclic graphs with the first two smallest F-indices, respectively.