For a connected graph , the reduced second Zagreb index is defined as
where and denote the degrees of vertices and in graph , respectively. We determine the extremal graphs among all connected graphs of order and with edges with respect to , and obtain the first ten largest for connected graphs of order . Moreover, we characterize the sharp upper bound on for all connected bipartite graphs with given connectivity . Finally, the extremal graphs with respect to are determined in all connected bipartite graphs with matching number .
"On the reduced second Zagreb index of graphs." Rocky Mountain J. Math. 50 (3) 975 - 988, June 2020. https://doi.org/10.1216/rmj.2020.50.975