The arithmetic-geometric index of a graph is defined as half the sum of the matrix elements of its arithmetic-geometric matrix.
Arithmetic-Geometric Index
See also
Arithmetic-Geometric MatrixExplore with Wolfram|Alpha
References
Cui, S.-Y.; Wang, W.; Tian, G.-X.; and Wu, B. "On the Arithmetic-Geometric Index of Graphs." MATCH Commun. Math. Comput. Chem. 85, 87-107, 2021.Guo, X. and Gao, Y.-B. "Arithmetic-Geometric Spectral Radius and Energy of Graphs." MATCH Commun. Math. Comput. Chem. 83, 651-660, 2020.Milovanović, I. Ž.; Matejić, M. M.; and Milovanović, E. I. "Upper Bounds for Arithmetic-Geometric Index of Graphs." Sci. Pub. State Univ. Novi Pazar A 10, 49-54, 2018.Molina, E.D.; Roodríguez J.M.; Sánchez J. L.; and Sigarreta, J. M. "Some Properties of the Arithmetic-Geometric Index." Symmetry 13, 857, 2021.Shegehall, V. S. and Kanabur, R. "Arithmetic-Geometric Indices of Path Graph." J. Math. Comput. Sci. 16, 19-24, 2015.Vujošević S.; Popivoda, G.; Vukićević; Furtula, Ž. K.; and Škrekovski, R. "Arithmetic-Geometric Index and Its Relations With Geometric-Arithmetic Index." Appl. Math. Comput. 391, Paper 125706, 2021.Vukićević, Ž. K.; Vujošević, S.; and Popivoda, G. "Unicyclic Graphs With Extremal Values of Arithmetic-Geometric Index." Disc. Appl. Math. 302, 67-75, 2021.Zheng, R.; Su, P.; and Jin. S. "Arithmetic-Geometric Matrix of Graphs and Its Applications." Appl. Math. Comput. 42, 127764, 1-11, 2023.Cite this as:
Weisstein, Eric W. "Arithmetic-Geometric Index." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Arithmetic-GeometricIndex.html