The sum of the squares of the degrees of vertices and the sum of the products of degrees of adjacent vertices have been introduced as topological indices. They are of interest from both applied and pure mathematical points of view. Given their close relations and rather similar behaviors, we examine the difference between these two indices in this note, presenting extremal results as well as some interesting properties.
Wang, H., & Yuan, S. (2016). On the sum of squares of degrees and products of adjacent degrees. Discrete Mathematics, 339(4), 1212–1220. https://doi.org/10.1016/j.disc.2015.11.013