General properties on Sombor indices

The Sombor index SO, the reduced Sombor index SOred, and the average Sombor index SOavg have been introduced recently, and it was shown that they have good predictive potential in Mathematical Chemistry. We obtain in this work several new lower and upper bounds of these indices. Specifically, we find inequalities between SO and SOred and characterize the graphs where equality occurs. Also, we present inequalities for SO and SOred involving other topological indices, such as the first and second (variable) Zagreb indices and the forgotten index. Finally, we find bounds for SOavg.