Select > Boundary Entities ... command select poly-vertices or poly-faces around selected boundary.

1.

Select Select > Boundary Entities in the menu or click the icon  in the toolbar. 

2.

Change the Type To Select to Poly-Faces and select the boundary.

3.

Click OK. The poly-faces around boundary are selected.

·   Type To Select – You can select poly-faces or poly-vertices around the selected boundary.

·   Seed Boundaries – Select boundaries that can be used to find poly-vertices or poly-faces in the model view.