For a simple connected graph G of order n having distance signless Laplacian eigenvalues
\rho _1^Q \ge \rho _2^Q \ge \cdots \ge \rho _n^Q
, the distance signless Laplacian energy DSLE(G) is defined as
DSLE\left( G \right) = \sum\nolimits_{i = 1}^n {\left| {\rho _i^Q - {{2W\left( G \right)} \over n}} \right|}
where W(G) is the Weiner index of G. We show that the complete split graph has the minimum distance signless Laplacian energy among all connected graphs with given independence number. Further, we prove that the graph Kk ∨ ( Kt∪ Kn−k−t),
1 \le t \le \left\lfloor {{{n - k} \over 2}} \right\rfloor
has the minimum distance signless Laplacian energy among all connected graphs with vertex connectivity k.