Applications of Radon’s inequalities to generalized topological descriptors

Given a graph G , many of its topological descriptors have the additive form D p ( G ) = (cid:80) i c pi , where the c i s are positive parameters associated with G , and p is an arbitrary real number. Sometimes these expressions are generalizations of descriptors with the simpler form D ( G ) = (cid:80) i c i . It is shown how Radon’s inequality and its refinements can be used to find a variety of bounds among members of these families of generalized descriptors. The particular case of sums of powers of normalized Laplacian eigenvalues is thoroughly discussed.