Select the boundary loop adjacent to the faces connected to a top/center vertex

boundary_from_top_vertice.py

import bpy

addon_keymaps = []

def main(context):
    bpy.ops.mesh.select_more()
    bpy.ops.mesh.region_to_loop()

class BoundaryFromTopVertice(bpy.types.Operator):
    """Boundary loop from top poked faces vertice"""
    bl_idname = "vertex.boundary_from_top_vertice"
    bl_label = "Boundary loop from top poked faces vertice"

    @classmethod
    def poll(cls, context):
        return context.active_object is not None

    def execute(self, context):
        main(context)
        return {'FINISHED'}


def register():    
    wm = bpy.context.window_manager
    km = wm.keyconfigs.addon.keymaps.new(name='Window')
    kmi = km.keymap_items.new(BoundaryFromTopVertice.bl_idname, 'T', 'PRESS', alt=True)    
    addon_keymaps.append((km, kmi))
    
    bpy.utils.register_class(BoundaryFromTopVertice)


def unregister():
    
    for km, kmi in addon_keymaps: km.keymap_items.remove(kmi)
    addon_keymaps.clear()
    
    bpy.utils.unregister_class(BoundaryFromTopVertice)


if __name__ == "__main__":
    register()

    # test call
    #bpy.ops.object.simple_operator()