THE SECOND AND THIRD GEOMETRIC-ARITHMETIC INDICES OF UNICYCLIC GRAPHS‡

Recently, G. Fath-Tabar, B. Furtula and I. Gutman (A new geometric-arithmetic index, J. Math. Chem. 47, 477–486, 2010) proposed the second geometric-arithmetic index GA2 and B. Zhou, I. Gutman, B. Furtula and Z. Du (On two types of geometric-arithmetic index, Chem. Phys. Lett. 482, 153–155, 2009) put forward the third geometric-arithmetic index GA3, respectively. In (Gutman, I. and Furtula, B. Estimating the second and third geometric-arithmetic indices, Hacet. J. Math. Stat. 40 (1), 69–76, 2011), inequalities between GA2 and GA3 for trees, with the number of vertices and the number of pendent vertices, were obtained by I. Gutman and B. Furtula. In this paper, we obtain inequalities between the two indices for unicyclic graphs.