On Inequalities for the Euler Sombor Index

The Euler Sombor index of a graph is a recently introduced and intensely studied topological index.In this paper, relations between the Euler Sombor index and the first Zagreb index M1 are established.A series of upper and lower bounds for the Euler Sombor index in terms of various graph parameters and other topological indices are also derived.Moreover, a fast algorithm is provided for estimating the Euler Sombor index in terms of M1.Furthermore, new upper and lower bounds for the forgotten index and the sigma index are established in terms of the second Zagreb index and other graph parameters, which are stronger than previously reported ones.