The Second and Third Geometric-Arithmetic Indices of Unicyclic Graphs

Year 2011, Volume: 40 Issue: 4, 555 - 562, 01.04.2011

Ping Liu Bolian Liu

Abstract

Recently, G. Fath-Tabar, B. Furtula and I. Gutman (A new geometricarithmetic 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 geometricarithmetic 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.

Keywords

Distance between vertex and edge, Geometric-arithmetic index, Unicyclic graph, 2000 AMS Classification: 05 C 12

The Second and Third Geometric-Arithmetic Indices of Unicyclic Graphs

Abstract

References

• Fath-Tabar, G., Furtula, B. and Gutman, I. A new geometric-arithmetic index, J. Math. Chem. 47, 477–486, 2010.
• Furtula, B. and Gutman, I. Geometric-arithmetic indices, in: I. Gutman, B. Furtula (Eds.), Novel Molecular Structure-Descriptors - Theory and Applications I, Univ. Kragujevac, Kragu- jevac, 137–172, 2010.
• Gutman, I. and Furtula, B. Estimating the second and third geometric-arithmetic indices, Hacet. J. Math. Stat. 40 (1), 69–76, 2011.
• Vukiˇcevi´c, D. and Furtula, B. Topological index based on the ratios of geometrical and arith- metical means of end-vertex degrees of edges, J. Math. Chem. 46, 1369–1376, 2009.
• Zhou, B., Gutman, I., Furtula, B. and Du, Z. On two types of geometric-arithmetic index, Chem. Phys. Lett. 482, 153–155, 2009.