There is one special node in DNS, called the root node. This is the one node that has no parents, at the top of the upside down tree. All other nodes have exactly one parent. The root node is also the only one that has an empty label.
Nodes can have zero or more children. There's nothing special about a node that has no children, although sometimes it is referred to as a Leaf Node.
Nodes that have the same parent are sometimes called sibblings. Such nodes cannot have the same label.