Harmonic-Arithmetic Index of Unicyclic Graphs
نویسندگان
1 School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China
2 School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China
3 School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China
doi
10.22052/ijmc.2024.255486.1909چکیده
Let G=(V(G),E(G)) be a graph. The harmonic-arithmetic index of G is defined as $HA(G)=\sum_{uv\in E(G)}\frac{4d_{G}(u)d_{G}(v)}{(d_{G}(u)+d_{G}(v))^2}$, where $d_{G}(u)$ is the degree of a vertex $u\in V(G)$. In this paper, we consider the upper and lower bounds of the harmonic-arithmetic index of unicyclic graphs with a fixed order. Furthermore, the graphs attaining the extremal values are also characterised.
