Bounds on the Arithmetic-Geometric Index

The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point of view. The aim of this paper is to obtain new bounds of the arithmetic-geometric index and characterize the extremal graphs with respect to them. Several bounds are based on other indices, such as the second variable Zagreb index or the general atom-bond connectivity index), and some of them involve some parameters, such as the number of edges, the maximum degree, or the minimum degree of the graph. In most bounds, the graphs for which equality is attained are regular or biregular, or star graphs.

[1]  S. Nikolic,et al.  On Variable Zagreb Indices , 2004 .

[2]  D. Vukicevic,et al.  Bond Additive Modeling 1. Adriatic Indices , 2010 .

[3]  Ante Graovac,et al.  Augmented Zagreb index , 2010 .

[4]  Jose Maria Sigarreta,et al.  Spectral properties of geometric-arithmetic index , 2016, Appl. Math. Comput..

[5]  D. Vukicevic,et al.  Bond Additive Modeling 2. Mathematical Properties of Max-min Rodeg Index , 2010 .

[6]  Kinkar Chandra Das,et al.  On the first geometric-arithmetic index of graphs , 2011, Discret. Appl. Math..

[7]  B. Wu,et al.  On the arithmetic-geometric index of graphs , 2020, 2010.03748.

[8]  Ernesto Estrada,et al.  AN ATOM-BOND CONNECTIVITY INDEX : MODELLING THE ENTHALPY OF FORMATION OF ALKANES , 1998 .

[9]  I. Gutman,et al.  Comparative analysis of symmetric division deg index as potentially useful molecular descriptor , 2018 .

[10]  László Csató,et al.  Measuring centrality by a generalization of degree , 2015, Central Eur. J. Oper. Res..

[11]  I. Gutman,et al.  Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons , 1972 .

[12]  D. Vukicevic,et al.  Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges , 2009 .

[13]  H. Wiener.  Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[14]  G. Fath-Tabar,et al.  Some Bounds on GA1 Index of Graphs , 2011 .

[15]  I. Gutman,et al.  Survey on Geometric-Arithmetic Indices of Graphs , 2011 .

[16]  Riste Škrekovski,et al.  Arithmetic-geometric index and its relations with geometric-arithmetic index , 2021, Appl. Math. Comput..

[17]  M. Randic.  Characterization of molecular branching , 1975 .

[18]  V. Shigehalli,et al.  Computation of New Degree-Based Topological Indices of Graphene , 2016 .

[19]  J. M. Sigarreta,et al.  CMMSE: A new approximation to the geometric–arithmetic index , 2017, Journal of Mathematical Chemistry.

[20]  I. Gutman,et al.  Degree-based energies of graphs , 2018, Linear Algebra and its Applications.