The Second and Third Geometric-Arithmetic Indices of Unicyclic Graphs

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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,

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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.