Some results on the reciprocal sum-degree distance of graphs

Abstract

In this contribution, we first investigate sharp bounds for the reciprocal sum-degree distance of graphs with a given matching number. The corresponding extremal graphs are characterized completely. Then we explore the $$k$$ -decomposition for the reciprocal sum-degree distance. Finally, we establish formulas for the reciprocal sum-degree distance of join and the Cartesian product of graphs.